How is the inheritance of a deceased woman, who left behind three children, divided, knowing that she bequeathed her gold for her Hajj and the remainder is to be distributed as charity?

If a woman dies leaving behind only three sons and no other heirs, then her estate is distributed among them by 'asabah (agnatic inheritance), and it is divided equally among them. Thus, it is divided into three shares, with each son receiving one share.