Do half-sisters inherit from their deceased brother who had offspring, given that the sisters' parents died before their brother?

The sister from the mother's side inherits on condition that the deceased has no father or son, and she receives one-sixth. If a man dies and leaves behind a full sister, a sister from the father's side, and a sister from the mother's side, then the full sister gets one-half, the sister from the father's side gets one-sixth, and the sister from the mother's side gets one-sixth. As for the remaining one-sixth, scholars differ concerning it: some are of the view that it goes to the public treasury (Bayt al-Mal), while others hold that it is returned to the sharers (dhawi al-furood). If the view of رد (return) is adopted, then the issue is out of five shares: three for the full sister, one for the sister from the father's side, and one for the sister from the mother's side.