Siman 489, Se'if 8

Sefiras Ha'Omer continued: one who forgot to count and is the shliach tzibbur

Shulchan Aruch, siman 489. The case we are about to discuss is not mentioned in the Shulchan Aruch itself; it is brought briefly in the words of the Sha'arei Teshuvah.

"One who forgot and did not count on one of the nights, and on the following night he was the shliach tzibbur and wishes to fulfill the obligation of others with his berachah."
(Sha'arei Teshuvah)

The proposed leniency: A shliach tzibbur who forgot to count one day argues: even though I cannot make the berachah for myself, since I am the shliach tzibbur, let me recite the berachah and fulfill the obligation of those who have not yet counted.
The assumption behind this: We are speaking of a time when the shliach tzibbur recited the berachah out loud and the congregation, or part of it, fulfilled its obligation through his berachah.

The basis of the leniency: all of Israel are responsible for one another

Birchos hamitzvos: Someone who has already fulfilled his own obligation may still recite the berachah on behalf of someone who is still obligated, because all of Israel are areivim, responsible for one another. As long as there is a Jew who has not performed the mitzvah, it is as though he himself has not performed it, since we are all one unit.
The example of shofar: A man who has already blown three or four times and comes to blow again for a congregation recites "asher kideshanu bemitzvosav vetzivanu lishmoa kol shofar," even though he personally has already fulfilled his obligation, because the congregation in front of him has not yet fulfilled theirs.
Why areivus is needed: A Jew who does not know how to recite the berachah cannot simply say, "Then I will not hear the shofar"; he is obligated in the mitzvah. Therefore someone else recites the berachah for him on the strength of areivus.
Birchos hanehenin are different: Someone eating an apple cannot ask his friend to recite the berachah for him, because this is not a birchas hamitzvah. Nobody is commanded to eat an apple, and a person who does not know the berachah can simply not eat it, or eat something whose berachah he does know.

Mitzvos performed with one's body versus a berachah, which is speech

There is no shelichus in the act of the mitzvah: A mitzvah that a person must perform with his own body, such as putting on tefillin, cannot be performed for him by someone else, even though in other areas we do find shelichus (for example, an agent who brings a get to another man's wife). The Torah established that these mitzvos must be done by the person himself; there is no agency in them and no fulfilling the obligation of others.
The berachah, which is speech: If the man puts on the tefillin himself, there is room to say that someone else may recite the berachah for him, since the berachah is an act of speech and all of Israel are areivim for one another. The whole discussion here is about matters of speech, where one person says the words in place of his fellow.
Blowing shofar: Even though the hearing is an act performed with one's own body, the berachah upon it is treated like any other matter of speech.
Two people who can blow: Two men already blew shofar in the morning elsewhere, and then came to shul: one recites the berachah for the congregation and the other blows. This is valid, and someone who does not know how to recite the berachah can fulfill his obligation through his fellow's berachah, on the strength of all Israel being areivim for one another.

The crux of the dispute: how do we define one who forgot to count

In all of these cases we are dealing with someone who performed the mitzvah and fulfilled his obligation, and therefore he can recite the berachah for others. But one who forgot a single day of Sefiras Ha'Omer is exempt from then on, and about this the poskim argue.

One side: His exemption is a total exemption from the outset. He is no longer part of the matter at all, like a minor, and he is not considered obligated in the mitzvah; therefore he cannot recite the berachah and fulfill others' obligation.
The other side: Fundamentally he is obligated to count; it is only that "his mouth has been shut" and he cannot recite the berachah. He still belongs to the collective of Klal Yisrael and to the obligation of counting, so the areivus is intact in him and he can recite the berachah for others.
Distinguishing between the two exemptions: One who blew shofar in the morning performed the mitzvah and is simply not obligated a second time, whereas one who forgot to count did not perform the mitzvah and is exempt from the outset from the rest of the count. This is a valid argument, but the other side responds that fundamentally he too is obligated; he just has no berachah in his mouth.

The counting itself: Even one who forgot may continue to count without a berachah ("today is seven days of the Omer"), and there is nothing at all wrong with that. The question concerns the berachah alone.

The words of the poskim (Sha'arei Teshuvah, siman 489)

"And regarding one who forgot and counted without a berachah, the Pri Chadash wrote that he cannot serve as shliach tzibbur to fulfill others' obligation; and the Mikra'ei Kodesh disagrees with him... And the Birkei Yosef cites the Knesses HaGedolah and the Semag, and the Beis David like the Pri Chadash, and he concludes: 'and we are small.'"
(Sha'arei Teshuvah)

Pri Chadash: One who forgot and counted without a berachah cannot serve as shliach tzibbur to fulfill others' obligation with his berachah.
Mikra'ei Kodesh: Disagrees, and holds that he may indeed serve as shliach tzibbur and fulfill others' obligation.
Birkei Yosef (the Chida): Cites the Knesses HaGedolah and the Semag, and the Beis David in agreement with the Pri Chadash, and concludes "and we are small," meaning that he cannot serve as shliach tzibbur to fulfill others' obligation, because he is exempt from the outset.

The scope of the dispute: This is a dispute from one extreme to the other: some say he can and some say he cannot. The Sha'arei Teshuvah quotes the phrase "and we are small," but not in his own name, rather in the name of the Birkei Yosef.

In practice

Do not rely on this solution: A rav or a shliach tzibbur who forgot to count should not rely on his being the shliach tzibbur in order to recite the berachah and fulfill others' obligation, since the matter is disputed.
A different approach: He should ask someone else to count with a berachah before or during davening, and he should stand next to him, hear the berachah and answer amen. He does not fulfill his obligation with this berachah, but he has heard a berachah, and he then continues counting without a berachah.
The drawback: The advice itself is fine, but it does not solve the rav's embarrassment at having to ask someone else in front of the congregation.
The day he missed: It is lost, and there is no way to repair it.
Bottom line: There is no clear-cut ruling here, and there are those who are lenient.

Additional cases: a convert and a bar mitzvah boy

A convert who converted during the days of the Omer

"And likewise a convert who converted during the days of the Omer counts without a berachah; and if he converted on the first day of the Omer, he counts that day without a berachah and afterwards with a berachah."
(Sha'arei Teshuvah)

What this means: A convert who converted in the middle of the days does not recite a berachah on the counting, since he did not count the earlier days. We see from here that he is not permitted the berachah.
Converted on the first day: He lost only one day, so he counts that day without a berachah, and from then on with a berachah.

A boy who becomes bar mitzvah during the days of the Omer

This is not a mishap: The boy did not forget and did not miss anything; he simply entered the obligation in the middle, and that is an entirely different story.
The reason he continues with a berachah: Since he counted all the previous days as part of chinuch, and even recited the berachah on them, continuing to count with a berachah is no worse than what he had been doing until now.
The difference from the convert: The convert did not count at all beforehand, whereas the boy was counting the whole time as part of chinuch.

A woman and Sefiras Ha'Omer

The root of the question

A man's obligation: Sefiras Ha'Omer nowadays is a matter of doubt whether it is d'Oraisa or d'Rabbanan.
A woman's obligation: Some exempt her, since this is a mitzvas aseh shehazman gramah, a time-bound positive mitzvah.
Whatever the Rabbanan enacted: Even if the counting is only d'Rabbanan, whatever the Rabbanan enacted they enacted along the lines of the Torah law; so if under Torah law a woman is exempt from time-bound positive mitzvos, here too she would be exempt.
The other side: Some say this is not a time-bound positive mitzvah at all, as will be explained when we define the category.

Defining a time-bound positive mitzvah: a halachic obstacle or a practical one

Defining the rule: A mitzvah whose obligation is caused by time, such as tefillin, which are not worn at night. There the obstacle is halachic. So too sitting in a sukkah after the days of the festival: the sukkah is still standing where it was, but halachically there is no mitzvah in it.
Kiddush levanah: On the surface this too is a time-bound mitzvah, and indeed a woman does not recite kiddush levanah. But some say it is not a time-bound positive mitzvah, because the reason one cannot say it during the day is not a halachic obstacle but simply that the moon is not visible. (Toward the middle of the month the moon is visible even in the afternoon; in any case there are days in the month when it cannot be seen at all.)
Bikkurim: Bikkurim are not brought on Purim, which would seem to make it a time-bound mitzvah, but the reason is that at that time of year there simply are no bikkurim in reality. Bikkurim exist in Eretz Yisrael around Shavuos and a bit afterwards; this is a practical obstacle, not a halachic one.
Sefiras Ha'Omer: According to this explanation it is not a time-bound positive mitzvah, since we count from Pesach until Shavuos, and after that there is no Omer at all. The obstacle is not halachic but simply that it is not the time of the Omer.
Conclusion of the discussion: This is a debate, and there is no clear ruling to be issued.

(Incidentally, a woman is not exempt from tefillah; she is obligated to daven once a day.)

Can a woman fulfill her husband's obligation

If she is obligated like a man: If we say that a woman is obligated in the counting just like a man, she can fulfill his obligation for him.
If the counting is optional for her: Most of the Acharonim wrote that she is exempt because it is a time-bound positive mitzvah, and even if she wishes to count it is merely optional; and one for whom the mitzvah is optional cannot fulfill the obligation of one who is obligated.
"Usefartem lachem": From the words of the Mishnah Berurah at the beginning of the siman, two explanations of "lachem" emerge. One explanation: it is not the beis din that counts for everyone, but rather each and every person counts for himself. The second explanation: in Sefiras Ha'Omer there is no shelichus in the act of counting itself, and one person cannot count on behalf of his fellow.
The practical difference: According to this, even a woman who is obligated like a man cannot count on behalf of someone else. The question remains only regarding the berachah, and it is possible that she can recite it.

Se'if 9: counting after Kiddush in shul

"On Friday night and on the night of Yom Tov, we recite the berachah and count after Kiddush in the shul."
(Shulchan Aruch)

Not practiced today: Nowadays we do not make Kiddush in shul, so this halachah is not practically relevant. But in the times when they did make Kiddush in shul, they counted Sefiras Ha'Omer after the Kiddush.
The difficulty: The rule is that the more frequent precedes the less frequent, and seemingly Sefiras Ha'Omer is more frequent than this Kiddush: over the forty-nine days of the count we count every single day, while during those same days there are at most seven such Kiddushim.
The underlying question: The comparison depends on how we define "more frequent," and there is no simple ruling on this.

In passing · What span of time determines what is "more frequent"

The root of the question: Is frequency measured according to the stretch of time we are currently in (fifty days, four months), or according to the entire year?
Reading from three sifrei Torah: On Shabbos Parshas HaChodesh that falls on Rosh Chodesh we read the weekly parshah, then Rosh Chodesh (twelve times a year), and then Parshas HaChodesh (once a year). This example does not resolve the question, since however you measure it the numbers are not equal and there is no dispute about it.
Rosh Chodesh Elul: On the second day of Rosh Chodesh Elul we begin saying "L'David Hashem ori v'yish'i," and we say it for about thirty days, while on Rosh Chodesh itself we say "Barchi Nafshi" one time; nevertheless, we say Barchi Nafshi first.
- One explanation: Barchi Nafshi belongs to the Shir shel Yom, and the whole Shir is a single unit; therefore it is not included in the question of frequency at all.
- A further explanation: Frequency is measured over the entire year. Barchi Nafshi is said every Rosh Chodesh, at least twelve times, and sometimes eighteen times when Rosh Chodesh is two days, while "L'David Hashem ori v'yish'i" is said during one month only. So Barchi Nafshi is more frequent over the course of the year, even though during this particular month it is said less often.
The same on Shabbos: We say the Shir shel Yom and then Barchi Nafshi, and if it is Rosh Chodesh the order is the same, because Barchi Nafshi comes as part of the Shir shel Yom.