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.
As long as the deceased has debts, then these should be paid off before dividing the estate among the eligible heirs because the repayment of debts is given precedence over the right of the heirs in the deceased’s estate. Allaah, The Exalted, says (what means): {… after any bequest he [may have] made or debt…} [Quran 4:11]
The Kuwaiti Encyclopedia of Islamic Jurisprudence reads:
"It is incumbent on the heirs to pay off the debts of the deceased before dividing the deceased’s estate; Allaah, The Exalted, says (what means): {… after any bequest he [may have] made or debt…} [Quran 4:11] This is according to the scholarly consensus so as to clear the deceased from his liability or so that his skin would cool down, as mentioned in the hadeeth of the Prophet …"
Also, if the deceased did not perform (the obligatory) Hajj although he was financially and physically able to do it, then the heirs are obliged to deduct the expenses of Hajj from the estate (to be paid for someone to perform Hajj on behalf of the deceased) before distributing the estate among themselves; and this is the opinion that we adopt at Islamweb. The author of Ar-Rawdh Al-Murbiʻ (a book of the Hanbali School of jurisprudence) wrote:
"The wasiyy (i.e. the executor of the will of the deceased), the heir, or the judge has to deduct the obligatory rights, such as debt, Hajj expenses, and other rights like zakah, vows, expiation, from the whole estate of the deceased, even if he did not make a bequest to that effect; for Allaah, The Almighty, says (what means): {...after any bequest he [may have] made or debt...} [Quran 4:11]"
If the estate is not sufficient to cover both the Hajj expenses and repayment of debts, then the Muslim scholars held different opinions regarding which of the two should be given precedence. The Kuwaiti Encyclopedia of Islamic Jurisprudence reads:
"Jurists differed as to which of the two liabilities should be paid first if the estate is not sufficient to cover both of them (i.e. Hajj expenses and repayment of people's debts); the Hanafi jurists held that the debts owed to Allaah are waived with death unless the deceased stated their repayment in his will, as will be clarified later. The Maaliki jurists, on the other hand, held that the payment of debts owed to people should be given precedence over those owed to Allaah because the rights due to Allaah are subject to His forgiveness, whereas a right due to a human must be fulfilled, unless he (its owner) relinquishes it; or because Allaah is not in need of anything while people are in need of their rights. The Shaafiʻi jurists held that the rights of Allaah should take precedence over the rights due to humans if the estate is not sufficient to repay both. They relied on the following Ahaadeeth: the Prophet, sallallaahu ʻalayhi wa sallam, said, 'The debt of Allaah has more right to be fulfilled.” He, sallallaahu ʻalayhi wa sallam, also said: 'Fulfill the due rights of Allaah over you; verily, He has more right to fulfillment.'"
Ibn ʻUthaymeen said:
"Some scholars held that both are to be repaid proportionally (i.e. a share should be deducted for the repayment of the debts owed to Allaah and another to repay the debts owed to people). Both liabilities should be repaid because both constitute debts to which the deceased is liable; none of them should be given priority over the other. This is the opinion held by the Hanbali jurists, and this is the correct opinion in this regard." [Sharh Az-Zaad]
After deducting the debts and expenses of Hajj, the remainder is to be divided among the eligible heirs as per the Islamic sharee'ah. If the deceased did not leave behind except those mentioned in the question, then the deceased’s wife gets one fourth of the estate as a fixed share because the deceased has no children; Allaah, The Exalted, says (what means): {…And for the wives is one fourth if you leave no child…} [Quran 4:12]
The remainder of the estate is to be given to the deceased’s full brother by virtue of taʻseeb (i.e. by virtue of 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." [Al-Bukhari and Muslim]
The nephew from the full brother and cousins from the full paternal uncle have no shares in the inheritance because they are wholly excluded by the existence of the full brother.
Hence, the estate should be divided into four shares; the deceased’s wife gets one share and the full brother gets three shares.
Allaah Knows best.