Is it permissible for a Christian son to inherit from his Muslim father after making the father believe that he is Muslim? Is the father sinful for convincing him of that? Is it permissible for him to manage his properties? Is it permissible to accept a gift from him?

If the son is Christian, it is reprehensible to officially register him as Muslim, due to the transgressions this entails concerning rights such as inheritance and guardianship in marriage. A Christian does not inherit from a Muslim, based on the Prophet's (peace and blessings be upon him) saying: "A Muslim does not inherit from a disbeliever, nor does a disbeliever inherit from a Muslim." What your father did by helping a Christian take a Muslim's money is considered reprehensible, and he must repent. He is not permitted to dispose of these funds because they do not belong to him; rather, they must go to their rightful heirs among the Muslim inheritors or to the public treasury (Bayt al-Mal). Likewise, it is not permissible to accept a gift from these wrongfully inherited funds, because it is usurped money.