Is it permissible for a brother and his needy sister to divide the money saved by their mother without giving any to their other financially well-off brothers and sisters? And how can the mother divide this money if that is not permissible?

Allah the Almighty has made it obligatory to be just among children in giving gifts, whether male or female. If a parent favors some of his children, he must be just among them either by reclaiming the gift or by giving to the others until justice is achieved. The mother in this prohibition is like the father. The Shari'ah-compliant justice in giving gifts is that the male receives the share of two females, for there is nothing more just than the division ordained by Allah the Almighty. It is permissible for the father or mother to give to one child without the others if the children are adults and mature, with their consent and without embarrassment, provided that their consent is given willingly and not out of fear.