How is the lawful estate of the deceased distributed when there is a father, a daughter, a wife, a full brother, two full sisters, a will stipulating one-third of the estate for the sake of Allah Almighty, in addition to the absence of a full paternal uncle for 23 years?

The missing paternal uncle does not inherit because he is excluded by the father. The will "for the sake of Allah" is to be spent on charitable acts for the poor and needy, and it is valid if it does not exceed one-third, and it is disbursed before the division of the inheritance. The remaining inheritance is divided among the father (one-sixth as a fixed share and the remainder by residuary right), the wife (one-eighth), and the daughter (one-half).