Imagine the following scenario: a young man grows up as an unaffiliated Jew (non-Cohen Levite). He engages in sexual intercourse with a goy whom he gets engaged to. During the engagement, the young man discovers his Jewish roots and becomes a Baal teshuva. He separates from his ex fiancé and spends time in yeshiva. After over a year of separation, She undergoes an orthodox conversion. Is it permissible for the man to marry the converted woman (whom he previously had sexual relations with)? Can you also provide sources for the answer.
The mishnah and gemorah say that if there is a rumor the a Jew has been with a non Jewish female he cannot marry her after conversion. There is a dispute amonst the Rishonim as to why he lechatchilo cannot marry her. Rashi explains that by marrying her he is justifying the rumor, but the Ramban and Rashbah explain that if her marries her people will say that she converted for ulterior motives. Therefore in a case where everybody already knows that he was living with her and she converted after they separated,all the Rishonim would agree that he can marry her as the above two reasons are not applicable. Of course if this is a practical question one should consult a reliable Rabbinical authority.
Gemorah Yevomos 24b, Rashi, Ramban and Rashbah. E:H 11:5, Teshuvas Divrei Chaim2:36, Teshuvas Toiv Taam Vedaas1:30, Teshuvas Pri Hasodeh 2:3, Teshuvas Achiezer 3:26, Teshuvas Imrey Yosher 1:176, Teshuvas Mishnas Sochir 53.