All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
The deceased's bequest to give her granddaughter her mother's share is in reality a bequest of something that does not legally exist; because the granddaughter's mother, i.e. the daughter who passed away before her mother, is not entitled to any share of the inheritance. This is because the one who dies first does not inherit from someone who dies later. Please, refer to Fatwa 90126. The jurists said that the beneficiary named in the bequest is not entitled to anything in this case.
Ibn Qudaamah said: "Chapter: if he (the testator) makes a bequest of the same share of someone who has no share, such as a bequest of his son's share, while he (the son) does not inherit due to him being a slave, or being of a different religion (than the testator), or with a share of his brother while the latter is prevented from inheriting from him, then the person named in the bequest does not get any part of the inheritance, because he is not entitled to any share according to the Islamic inheritance laws; such a person does not get any part of the inheritance. " [End of quote]
Therefore, if the deceased woman died leaving behind a husband, two sons, two daughters, one full-brother and one full-sister, and she did not leave any other heirs, then her husband gets one-fourth of the estate as his legal share due to the existence of direct heirs (children); Allaah says (what means): {But if they have a child, for you is one fourth of what they leave, after any bequest they [may have] made or debt.} [Quran 4:12]
The remainder should be divided among the two sons and the two daughters by Ta‘seeb (by virtue of having a paternal relation with the deceased and not having an allotted share, so they get what is left after the allotted shares have been distributed), with the male receiving twice the share of the female; Allaah says (what means): {Allaah instructs you concerning your children [i.e. their portions of inheritance]: for the male, what is equal to the share of two females.} [Quran 4:11]
Therefore, the inheritance should be divided into 8 shares. The husband gets 2 shares, each son gets 2 shares and each daughter gets 1 share.
The full-brother and the full-sister do not get any part of the inheritance because they are prevented from the inheritance due to the existence of a son.
It should be noted that the division of inheritance is a serious and complex issue. It is not adequate to settle for a Fatwa to be issued according to the information provided by the questioner. Instead, you should refer the case to legitimate Islamic court for investigation; other heirs may be only discovered by careful investigation and would be discovered in the process. Moreover, the deceased may have left a will or may have been liable to debts or other obligations and liabilities of which the heirs are not aware. It is well-known that the settlement of debts and other liabilities are given precedence over the heirs' right to their shares in the estate. Therefore, you should not distribute the estate without referring the case to an Islamic court, if any exists, in order to secure the interests of the living and the dead alike.
Allaah Knows best.