Gemara

97b: The children of the female slave Yudan were freed. Rav Acha bar Yakov permitted them to marry each other's wives.

Objection (Rava): Rav Sheshes forbade this!

Rav Acha bar Yakov: He forbade, and I permit!

Version #1: If they are only paternal brothers (from different mothers), all agree that they are permitted. If they are only maternal brothers, all agree that they are forbidden. They argue about full brothers:

Rav Acha bar Yakov permits, since people consider them to be paternal brothers. They call them 'the sons of Ploni';

Rav Sheshes forbids, for people also call them 'the sons of Plonis (their mother).'

Version #2: Rav Acha bar Yakov permits in all cases, even when they are only maternal brothers, because a convert is like a newborn baby.

98a (Rava): People say that a Mitzri (Nochri) has no father. This is not because Nochrim are immoral and we do not know who is his father. A Beraisa teaches that twins, who come from one drop of semen that split into two, do not do Chalitzah or Yibum!

Rather, the Torah considers the child to have no father because "Their flesh is flesh of donkeys, and their seed is like that of horses".

(Beraisa): If a boy was born after his mother converted but was conceived beforehand, he is considered a convert. He is forbidden to maternal relatives, but not to paternal relatives;

If he married his maternal sister or his father's maternal sister, he must divorce her. If he married his paternal sister or his father's paternal sister, they may stay married. If he married his mother's maternal sister, he must divorce her.

R. Meir says, if he married his mother's paternal sister, he must divorce her;

R. Meir says that he must divorce any relative on the mother's side, but he may keep any relative on the father's side.

Chachamim say, he may keep her.

He is permitted to the wife of his maternal brother, and the wife of his father's brother, and all other Arayos are permitted, i.e. even his father's wife.

22a - Question (Rava): Do Sheniyos (Arayos mid'Rabanan) apply to converts?

Answer (Rav Nachman): Even Arayos are forbidden to converts only so they will not say that they descended to a lower Kedushah. Certainly, there was no decree of Sheniyos!

(Rav Nachman): Maternal brothers who converted may not testify for each other. If they did, the testimony stands. Paternal brothers may testify for each other.

(Ameimar): Even maternal brothers may testify for each other.

We are more stringent about Arayos, for they pertain to every person. Testimony is received by Beis Din. (Beis Din will not err; they know that) a convert is like a newborn.

Rishonim

Rif and Rosh (4b and 2:2): Arayos are forbidden to converts only so they will not say that they descended to a lower Kedushah. Sheniyos are permitted. We are more stringent about Arayos than testimony, for Arayos pertain to every person, but testimony is received by Beis Din. A convert is like a newborn.

Nimukei Yosef (DH Yerushalmi and DH Omar): Sheniyos did not apply when he was a Nochri, so they are permitted now without concern for Chilul Hash-m. A convert has maternal kinship, for it is Vadai his mother. Nevertheless, the testimony is valid b'Di'eved because he is like a newborn. However, not everyone knows this. Everyone gets married, so if we permit Arayos to converts, perhaps also Yisraelim will marry Arayos.

Rosh (ibid.): We forbid all maternal Arayos to a convert, even those who are permitted to Nochrim, lest he be confused with a Yisrael.

Rif and Rosh (11:2): All permit a convert to marry the wife of a solely paternal brother, but not the wife of a solely maternal brother. Rav Acha bar Yakov permits the wife of a full brother, and Rav Sheshes forbids. Some say that Rav Acha permits even a maternal brother's wife, because a convert is like a newborn baby.

Nimukei Yosef (DH Gemara): There are three ways in which relatives are forbidden to a convert. (1) If they were born in Kedushah, they have She'er (kinship) of the mother mid'Oraisa. If also conception was in Kedushah, they also have She'er of the father. (2) All Arayos forbidden to Benei No'ach are forbidden lest people say that they had greater Kedushah before conversion than after. This applies only to Arayos forbidden mid'Oraisa. There is no concern for Arayos that Nochrim themselves forbid. (3) Something that is forbidden to Yisraelim we forbid to converts, lest people come to err.

Nimukei Yosef (ibid.): If a couple converted, he may keep her or divorce her. She is permitted to others even in his lifetime (if they did not have Bi'ah after converting). Even though Be'ulas Ba'al applies to Benei No'ach (a woman becomes a man's wife through Bi'ah), conversion uprooted the marriage. If we did not say so, a Get would not permit her, since it does not permit a Bas No'ach! The only Ervah due to marriage among Nochrim is Eshes Av, according to R. Akiva. We learn from Yakov and Yehudah that there is no Isur of Eshes Ach or a daughter-in-law. Therefore, we do not forbid Eshes Ach of a convert lest people say that they came to a lower Kedushah. Even though she was forbidden (after Nisu'in) due to Eshes Chaveiro, everyone knows that this ended when she converted. Everyone knows that there is no brotherhood when the birth was without Kedushah.

Rosh: We need not forbid the wife of a solely paternal brother. There is no concern lest they be confused with Yisraelim, for everyone knows that a Nochri does not have a (Halachic) father. We are not concerned lest they say that being a Yisrael is more lenient than being a Nochri, because he had no kinship before converting. All Arayos forbidden to Yisrael apply to maternal brothers, lest they be confused with Yisraelim. This is whether one or both of them were born without Kedushah (before their mother converted). The Ri holds that if one of them had full Kedushah (conception and birth) and the other had no Kedushah, we are not concerned lest they be confused with Yisraelim.

Beis Yosef (DH u'Mah she'Chosav v'Ein): Tosfos was unsure about this.

Rosh (ibid.): All Arayos forbidden to Benei No'ach are forbidden to paternal brothers, lest people say (that they had greater Kedushah before). This refers to the father's wife according to R. Akiva (Sanhedrin 58a), or the father's sister according to R. Eliezer. Each Tana permits the other of these two, for there is no concern for confusion or what people will say. BaHaG rules like R. Akiva, because R. Eliezer is Shemuti (from Beis Shamai). Some rule like R. Eliezer because Chachamim of R. Meir rule like him in Sanhedrin.

Rambam (Hilchos Isurei Bi'ah 14:12): Mid'Oraisa, a convert may marry his mother or maternal sister. Chachamim forbade this lest people say that they had greater Kedushah before they converted than afterwards, i.e. this was forbidden and now it is permitted. If a convert had Bi'ah with his Nochris mother or sister, it is like Bi'ah with a stranger.

Rambam (13): If a convert was married to his mother or maternal sister before conversion and they converted, we separate them, like we explained. If he was married to a different Ervah and they converted, we do not separate them. Mid'Rabanan, a convert is forbidden to his mother's relatives. He is permitted to his father's relatives, even if we know that they are surely his father's relatives, e.g. twins who surely have the same father. Therefore, a convert may marry the wife of his paternal brother or uncle, his father's wife or his daughter-in-law, even if she married his relative after they converted. Similarly, he is permitted to his mother's paternal sister, his paternal sister or his daughter after she converted. He may not marry his maternal sister, his mother's maternal sister, or his maternal brother's wife after his brother converted. If she was married to his brother before he converted, she is permitted.

Kesef Mishneh: We said (22a) that Arayos are forbidden to converts only so they will not say that they descended to a lower Kedushah. This refers to maternal relatives. Even though we permit paternal relatives, since we forbid new maternal relatives to them, people will not call this a lower Kedushah. They will say that conversion changes the laws. If the only concern were confusion with Yisraelim, Chachamim would not have decreed at all.

Rebuttal (Gra YD 269:2): The Rambam holds like Tosfos (22a DH Ervah), that we decree for both reasons. Everyone knows that there is no fatherhood of Nochrim, so there is no concern for confusion with Yisraelim, but 'they descended in Kedushah' applies. Confusion with Yisraelim is why we forbid all maternal relatives. The Rambam lists only Arayos forbidden even to Nochrim, for even b'Di'eved a convert may not stay married to them.

Poskim

Shulchan Aruch (YD 269:1): Mid'Oraisa, a convert may marry his mother or maternal sister who converted. Chachamim forbade this lest they say 'we had greater Kedushah before we converted than afterwards.' If a convert had Bi'ah with his Nochris mother or sister, it is like (any) Bi'ah with a Nochris.

Shulchan Aruch (2): If a convert was married to his mother or maternal sister before conversion and they converted, we separate them. If he was married to a different Ervah and they converted, we do not separate them.

Shach (2): Regarding other Arayos there is no confusion with Yisraelim, for they were married before conversion. They must separate for three months so we will know whether or not the child was conceived in Kedushah.