Is it valid for a husband to take back his wife after an irrevocable divorce (طلاق بائن) finalized by the marriage officiant (ma'dhun) and before the 'iddah (waiting period) ends, without a new contract or returning to the ma'dhun, given that there was an announcement among family and friends? And what is the necessary procedure to rectify this?

If a woman is divorced with an irrevocable (ba'in) divorce, it is not permissible for her to return to her husband except with a new marriage contract. The widespread knowledge of the matter among her family does not make it permissible for him. It is advisable to consult scholars to clarify the manner of divorce and to ask them before taking action, in order to avoid violating the Sharia (definition), especially in matters of marriage and divorce.