Is it permissible to deny the occurrence of a divorce that was not officially documented between the parents, in order to enable the mother to obtain her share of the inheritance, as compensation for the father's failure to provide for her throughout the years, and does sin result from that?

The occurrence or non-occurrence of divorce cannot be definitively ascertained without knowing the exact words uttered by the father. If the divorce is proven to have occurred according to Islamic law and the wife has been irrevocably divorced, then she does not inherit, and it is not permissible to resort to trickery to make her inherit. However, if the divorce did not occur according to Islamic law, then she does inherit, with the caveat that the marital bond is presumed to remain, and divorce is not established by doubt or conjecture. The widespread knowledge of divorce among relatives is not sufficient unless there are witnesses to the divorce. The resolution of disputes falls under the jurisdiction of Sharia courts or their representatives, due to their ability to hear from all parties and issue precise rulings. A mufti only hears from one party and cannot issue an accurate ruling in such cases. Therefore, it is advisable to refer the matter to the Sharia court to examine the occurrence of the divorce and its implications for the mother's inheritance or lack thereof.