Is a marriage with an opening chapter of the Quran (Al-Fatiha) and a dowry, which has resulted in children registered in the civil status, considered a legitimate marriage?

A lawful marriage is one that fulfills known conditions, and any contract lacking these conditions, or some of them, is invalid. Among these conditions is the form of the contract (the offer from the guardian and the acceptance from the husband). Reciting Al-Fatihah is not sufficient in its place. If the contract lacks this form, the marriage is invalid. However, the children are attributed to their father as long as both parents believe the marriage to be valid. The absence of official documentation of the contract does not affect the validity of the marriage.