Can a couple reunite after having been divorced three times, knowing that the first divorce was an innovated divorce (bid‘i) (during a period of purity in which intercourse occurred)?

The Sunnah regarding divorce is for a man to divorce his wife during a period of purity (tahr) in which he has not had intercourse with her. If a man divorces his wife with an innovated divorce (talaq bid'i) and considers it a divorce, then his divorce is valid and enforceable.

Sheikh Ibn Uthaymeen said: - If a question is posed about an innovated divorce while the woman is still in her waiting period (iddah), the fatwa given is that the divorce does not occur. - If a question is posed after the iddah has expired, the fatwa given is that the divorce does occur, and this is the view of the majority. - If a man divorces his wife three times, and he believes it is the final divorce, then if he divorces her while she is menstruating, the fatwa given is that she is irrevocably separated from him. - Sheikh Ibn Uthaymeen continued to issue fatwas affirming the occurrence of an innovated divorce for whoever believed it occurred.

Therefore, the husband has divorced his wife three times.