Is zakat obligatory on a donation fund established to help the family of a deceased person, given that it has reached the nisab and a hawl (year) has passed, and knowing that it is directed solely to this family? Is it considered like a charitable endowment on which zakat is not obligatory?

If the money has left the donor's responsibility, then there is no zakat due on it from him, nor from the poor person, because the poor person has not yet received it and it has not entered his possession. Rather, it has entered a general charitable fund over which the poor person has no authority; therefore, there is no zakat on this money.