What is the ruling on this marriage and the ruling on the divorce that occurred, and has the greater, irreversible divorce (al-baynunah al-kubra) taken place, and what are the implications of that, given that there are no documents proving this marriage?

Divorce during menstruation or during a period of purity in which intercourse has occurred is a forbidden, Bid'i (innovated) divorce, but it is effective according to the majority of scholars. If the husband writes a letter divorcing his wife, intending it to take effect, the divorce is valid. If he does not intend it, there is a difference of opinion. If the husband wrote the letter intending to divorce her, three divorces took place, and she became irrevocably separated from him (Baynunah Kubra). A man's marriage to a woman is valid if it fulfills the conditions and pillars of a lawful marriage, and the husband's intention to separate from the wife does not invalidate it. It is recommended to present the issue to the Sharia court or to reliable scholars. Documenting the marriage is essential to avoid corruption and the loss of rights.