What is the ruling of the Sharia regarding the return of a couple after the third divorce, which occurred by mutual agreement and the insistence of the wife, following reconsiderations and regret from both parties?

A wife is subject to divorce if she is under a marital bond at the time it occurs, such as a revocable divorcee (raj'iyyah) who is unanimously agreed to be subject to her husband's divorce. As for divorce after the marital bond has ceased, it does not take effect. If the marriage after the 'iddah (waiting period) was without the fulfillment of the pillars of validity, then it is void (laghw), and the third divorce does not take effect because it occurred after the cessation of the marital bond. If the wife was divorced three times while under a marital bond, she becomes irrevocably separated (baynunah kubra) and is not lawful for him until she marries another husband. If it was less than three divorces, he may take her back before her 'iddah ends. If her 'iddah has ended, she is not lawful for him except with a new contract. Divorce during menstruation, or post-natal bleeding (nifas), or multiple divorces within one period of purity, or occurring in a period of purity during which intercourse took place, or before reconciliation, or renewing the contract, is considered valid by the majority of scholars. It is advised to consult scholars directly for detailed rulings on such complex matters.