Daughter of pregnant convert also a convert?

Hi, If a woman converts while she is pregnant, is the child considered a convert when she is born, or a native-born Jew? Can that girl (whose mother converted after the girl was conceived but before she was born) marry a Cohen if her father is Jewish and not a convert with only her mother being a convert?

ב"ה Shalom, These types of questions, I answer only in theory since many variables are involved which need serious consideration and only an officiating Rabbi who is made known to all details may give the final word. As to your first question ,as far as fulfillment of the Torah and its commandments, the child is a full-fledged Jew as far and is considered part of the Jewish people. However, there are certain aspects in regard to monetary issues, inheritance, and certain laws of incest, in which different rules apply. As far as a Cohen, marrying the child who was conceived while not being Jewish but born Jewish, it is forbidden. Though the Shulchan Aruch (Even Ha'ezer 7:21 ) says that if a Jew married a woman convert, a cohen may marry the daughter conceived in this marriage, this applies only when he married her when she was already Jewish, but not in a case when the child was conceived in a relationship the Jew had with the woman while she was still gentile. All the Best