Does the son continue to receive the income from the apartment that his father gifted to him after the father's death, or does it become the property of the heirs, especially since there is a will from the father to his agent stating that the son should benefit from the apartment until the end of the year?

A father must be equitable among his children in giving gifts. If he fails to do so and gives one of his children an apartment to benefit from its rent without giving the others an equivalent, then he commits an injustice. In this case, the other children must forgive their father. It is not permissible for the beneficiary of the apartment to continue taking its rent after the father's death unless all heirs agree, including minors, as the guardian of minors must protect their rights. As for the father's will to his son to benefit from the apartment until the end of the year, this will is not valid for an heir unless the rest of the heirs permit it, and if there are minors among them, their guardian is not permitted to permit it.