Is the marriage of a man to a woman with whom he had previously engaged in marital relations while she was still married to another man, then she was divorced and her waiting period (iddah) ended, then he married her and paid her a dowry (mahr) and deferred dowry (mu'akhkhar), and he has children with her, considered a valid marriage Islamically? And what should he do if it is not?

A man and a woman who have committed adultery must repent and perform many righteous deeds, because this act is a grave sin, especially since the woman is married, which entails violating the sanctity of the husband and corrupting his bed.

Furthermore, repentance from a sin does not negate the right of the wronged party. Therefore, one must accumulate many good deeds to compensate those who were wronged in the Hereafter. Adultery with a married woman is a more severe sin than adultery with an unmarried woman, because it involves corrupting the husband's lineage and inflicting harm upon him; it is worse than taking money.

As for the marriage of the two adulterers, it is valid if it takes place after the 'iddah (waiting period) has ended and if the pillars of a lawful marriage are fulfilled.