Is it permissible for a father to disinherit one of his wives and her children by writing all of his wealth to his other wife, and is it permissible for this wife to favor one of her children over the others in the distribution of inheritance, and what is the ruling on the money taken by the eldest son in this case?

What your friend's father did by writing all his wealth in his wife's name to disinherit his other wife and her children is a forbidden act that warrants the Fire. He must be dealt with contrary to his intention; thus, all the money should be returned as an inheritance to be divided among all heirs according to Islamic law. Your friend's, his mother's, and his siblings' disposal of these funds is void because it belongs to all heirs. Therefore, what they took should be examined, and any amount exceeding their lawful share should be taken by the remaining heirs. As for a mother favoring one of her children in giving gifts without a legitimate Islamic justification, it is impermissible.