Peah, Chapter 4, Mishnah 6. This mishnah opens the discussion of the remaining gifts to the poor - the additional obligations of giving to the poor beyond peah.
"Nochri shekatzar es sadehu ve'achar kach nisgayer - patur min haleket umin hashich'chah umin hapeah":
A gentile who harvested the grain growing in his field, and after the harvest converted and became a righteous convert - from that point on he is obligated in the gifts to the poor, whereas beforehand he was exempt. For the grain he harvested while he was still a gentile he is exempt from three gifts:
Leket - the stalks that fall during the process of harvesting.
Shich'chah - a sheaf forgotten in the field.
Peah - the portion left over from the harvest.
The reason for the exemption: at the time he did the harvesting he was not Jewish, and he was not obligated in these mitzvos.
The opinion of Rabbi Yehudah:
"Rabbi Yehudah mechayev bashich'chah" - Rabbi Yehudah agrees regarding leket and peah, since these obligations take effect at the moment of the harvesting itself. The wording of the verses proves this: regarding leket it says "and the gleanings of your harvest," and regarding peah it says "and when you reap the harvest of your land... you shall not finish off the corner of your field to reap" - both gifts are tied to the act of harvesting.
Regarding shich'chah, however, he obligates him, and his reason is: "she'ein hashich'chah ela bish'as ha'immur" - the obligation of shich'chah is determined at the time a person makes the sheaves. Since he converted immediately after the harvest, presumably he did the gathering into sheaves when he was already Jewish, and therefore he is obligated in shich'chah.
The opinion of the Tanna Kamma:
The Tanna Kamma holds that just as the time of harvesting determines the obligation in leket and peah, so too it determines the obligation in the forgotten sheaf. Even though the gathering into sheaves takes place later, since the rest of the gifts to the poor depend on the harvesting, the obligation of shich'chah too is determined by the time of the harvest - whether or not he was obligated in the mitzvah at that moment.
In summary: In this mishnah we learned that a gentile who harvested his field and afterward converted is exempt from leket, from shich'chah and from peah, because at the time of the harvest he was not obligated in these mitzvos. Rabbi Yehudah obligates him in shich'chah, because its obligation is determined at the time of gathering into sheaves, which was already done after the conversion; the Tanna Kamma, however, holds that the obligation of shich'chah too is determined by the time of the harvest, like the rest of the gifts to the poor.