Is it obligatory to disburse all the money that a father gifted to his daughter for charitable purposes and for the benefit of Muslims, with the intention of absolving his responsibility, after discovering that its source was ill-gotten (embezzlement and bribery)? Or is it permissible for the daughter, or would she be sinful by possessing it?

Unlawful wealth is not permissible for the heirs of its possessor. If an heir is unaware of its amount, they should strive to estimate it. Otherwise, they should divide it in half and donate one half. If the unlawful wealth has a specific owner, it must be returned to them or to their heirs if they have passed away. As for the gift owned during the lifetime of the donor, the questioner incurs no sin in fully benefiting from it, because her father's wealth is mixed with both lawful and unlawful elements. Accepting a gift from someone whose wealth is mixed is disliked, but not unlawful according to the preponderant opinion. Some scholars say it is permissible if the lawful portion predominates over the unlawful, and unlawful if the unlawful portion predominates over the lawful.