Is it permissible for aunts to relinquish their share of inheritance to their brothers (the sons), and do the children of these aunts have the right to claim this inheritance in the future?

For a waiver of inheritance to be valid, the waiving party must be mature and of sound judgment, and their waiver must be free from coercion. If someone waives their share willingly and voluntarily, and they are mature and of sound judgment, then their waiver is enforceable. Among the reprehensible forms of coercion is coercing and abusing a woman to waive her right. Such a waiver is invalid, and the wealth acquired through it is unlawful, because the Prophet, peace and blessings be upon him, said: "The wealth of a Muslim person is not lawful unless it is given with their full consent." If their waiver is truly with full consent and without coercion, and they are mature and of sound judgment, then the waiver is valid; it is a gift from them to their brothers, and they are not permitted to retract it if its conditions have been met.