Is it permissible for a child born out of an illicit relationship to live with his mother after she marries the person who was a party to that relationship?

Sincere repentance is obligatory for the sin of adultery. Among the conditions of repentance is remorse for having committed the sin. The child is attributed to the husband, and there is no impediment to his remaining, with a warning against adoption. You may care for him, look after him, and raise him.