Is the money granted by the Algerian state to my mother—who married my father in 1961 CE and was nominally divorced in 1973 CE to preserve her martyred husband's pension—lawful after my father's death?

The grant given by the state to the mother: If it is deducted from her husband's salary, then it is an inheritance to be distributed among his heirs according to their shares. Your mother would receive one-eighth if he had children, and one-fourth if he had no children. If the grant is a special assistance for her, then it is her property to dispose of as she wishes. However, if it is conditioned upon her not marrying, then it is not permissible for her to take it after her marriage. If her husband dies and the condition returns, then it becomes permissible for her at that time as long as she does not marry. So, the matter revolves around the grantor's condition. As for the divorce declared by the father in court: If he did not utter words indicating divorce, then there is nothing against him. If he falsely admitted to it and did not actually pronounce it, then the preponderant opinion is that it takes effect judicially, not religiously, meaning his wife remains under his marital bond unless the matter is brought before a judge.