Do the children of a sister who died before the deceased inherit by virtue of a will stating, "that the children of his sister who died before him inherit as if she were still alive," given the existence of a wife, a full brother, and two full sisters?

In this matter, if the deceased left behind a wife, a full brother, and two full sisters, the wife receives one-fourth due to the absence of a lineal descendant. The remainder is distributed among the brother and the two sisters by ta'sib (agnatic inheritance), with the male receiving the share of two females. The inheritance is divided into 19 shares: 4 for the wife, 6 for the full brother, 3 for each full sister, and 3 for the children of the deceased sister. If the deceased sister was only a paternal sister, the will is invalidated, and the inheritance is divided into 16 shares with the same aforementioned distribution. If the sister was only a maternal sister, the inheritance is divided into 56 shares: 12 for the wife, 36 for the siblings (18 for the brother and 9 for each sister), and the will for the children of the deceased sister would be 8 shares. Inheritance matters must be referred to the Sharia courts for investigation to ensure there are no other heirs, wills, debts, or other rights.