What is the ruling on a wife upon whom a divorce has occurred, but she does not inform her husband of it, and he continues to cohabit with her as a husband and she becomes pregnant, then the truth is revealed through the testimony of upright witnesses? And do the children born from this relationship inherit?

Divorce can be conceived without the husband's knowledge in the case of a contingent divorce. If a contingent divorce occurs and the husband has sexual intercourse with his wife, it is treated as intercourse due to a شبهة (misconception/doubt), and the child is attributed to him, with all the rulings of a child from a valid marriage applying. The wife is sinful if she does not inform her husband of the divorce's occurrence. If the husband has sexual intercourse with his revocably divorced wife during her iddah (waiting period), she returns to him. There is no sin on the wife if her divorce was revocable, and there is no issue regarding the child being attributed to him.