Assalaamu alaykum. Please calculate the inheritance according to the following information: - Does the deceased have male relatives who are entitled to inherit: (A half brother [from his father]) Number 1 - Does the deceased have female relatives who are entitled to inherit: (A wife) Number 1 - Information about the deceased’s debts: (Did not perform Hajj despite having the financial ability, and no one performed it on his behalf yet.) (Debts to people)

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.

If the deceased was financially and physically able to perform the (obligatory) Hajj and passed away before performing it, then he bears a sin for failing to carry out this religious obligation. In this case, it is incumbent on the heirs to deduct the Hajj costs from the estate before distributing it, and that is to be paid to someone to perform the Hajj on behalf of the deceased. The same applies to the ʻUmrah, based on the scholarly view that it is obligatory; this is the preponderant view at Islamweb.

Moreover, the heirs are obliged to deduct the debts of the deceased and repay them before distributing the estate as well; Allaah, The Exalted, says (what means): {...after any bequest he [may have] made or debt...} [Quran 4:11]

If the deceased left no other heirs entitled to inherit other than those mentioned in the question, then the wife is entitled to one-fourth of the estate as a fixed share because the deceased has no descendants entitled to inherit. Allaah, The Exalted, says (what means): {...And for the wives is one-fourth if you leave no child...} [Quran 4:12]

The deceased’s paternal half-brother is entitled to the residue of the estate by virtue of taʻseeb (having a paternal relation with the deceased and not having an allotted share, so he gets what is left after the allotted shares have been distributed). The Prophet said, "Give the faraa'idh (shares prescribed in the Quran) to those who are entitled to receive them; and whatever remains should be given to the closest male relative of the deceased." [Al-Bukhari and Muslim]

Hence, the estate should be divided into four shares; the wife gets one share and the remaining three shares are for the half-brother (from the father’s side).

Lastly, it should be noted that the division of the inheritance is a serious and complex issue. It is not adequate to settle for a fatwa to be issued according to the information given by the questioner. Instead, you should refer the case to an Islamic court for further 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.