Assalamu alaykum respected Mufti Sahab and Shariah Board,
الجواب وبالله التوفيق
In case of a husband’s denial to issue talaq, the woman has to provide the proof of such talaq(i.e. two men or one man and two women witnesses). If the woman fails to provide said proof, or the requirement of the said number witnesses is not fulfilled then the husband has to perform a qasam(i.e. swear) and swear that he has not issued a divorce. In that case, his statement will be considered acceptable and a ruling will be made for the invalidity of divorce. However, if he had in fact issued a divorce but is using deception or lying to get back with his wife, then such an action will not make his wife halal upon him. He will be accountable for such actions in front of Allah Subhanahu Wa Ta‘ala. If he continues to live in that situation with his wife, its sin and the sin for establishing illegitimate relations with the woman will surely be upon him. In this situation, the ruling for the woman is that if she knows for a fact that the husband had issued three talaqs, and is swearing falsely to live together with the woman, then it is impermissible for the woman to let him gain control over her.
قال تعالی:فان طلقھا فلا تحل لہ من بعد حتی تنکح زوجاًغیرہ (القرآن)
المرأۃ کالقاضی اذا سمعتہ اواخبرھا عدل لا یحل لھا تمکینہ الخ (فتاوی دارالعلوم زکریا ص 119، ج4