Is it permissible to marry a woman who gave birth to a child out of wedlock (zina) and then married the fornicator, who subsequently divorced her? And can her husband raise her daughter, knowing that she is a child born out of wedlock (zina)? What is the position of his children towards her?

If a woman repents from adultery, it is permissible to marry her, because repentance erases what came before it, and due to the Prophet's (peace be upon him) saying: "The one who repents from sin is like one who has no sin."

As for a girl born out of wedlock (from zina), she is not attributed to the adulterer but is ascribed to her mother. If you marry the woman, the girl becomes your stepdaughter, forbidden to you (for marriage), and you will be rewarded for caring for her. If you have children with that woman, the girl will be their sister from their mother's side, because the lineage of a girl born from zina is firmly established with the mother.