Assalaamu alaykum. Please calculate the inheritance according to the following information:
- Does the deceased have male relatives who are entitled to inherit: (A cousin from a half paternal uncle) Number 1 (A husband)
- Information about the deceased’s debts: (Debts to people)
- Additional information: She has three nieces (her sister's daughters), two nephews (her sister's sons), and two full-cousin's sons

All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger. 

The nephews and nieces (i.e. the sons and daughters of the sister) do not get anything from the inheritance of their deceased maternal aunt because the daughters and sons of the sister are not among the heirs in principle; rather, they are among Thawul Arhaam (cognates or distant kindred).

The two full cousin’s sons are prevented from the inheritance by the existence of the cousin from the father’s side as he is closer to the deceased than them.

Since the deceased has debts owed to people, then these debts must be paid prior to the division of the inheritance because paying back the debts takes priority over the right of the heirs in the inheritance; Allah says in the verses about inheritance (what means): {…after any bequest he [may have] made or debt.} [Quran 4:11]

The Fiqh Encyclopedia reads:

“The debt of a human being is the debt owed to the slaves [of Allah], so paying back this debt from the inheritance and fulfilling it is an Islamic obligation on the heirs before they divide the inheritance between them; as Allah says (what means): {…after any bequest he [may have] made or debt.}, and there is a consensus among the scholars about this; this is in order that he [the deceased] will be acquitted from the rights of the people, or so that his skin becomes cool, as mentioned in a Prophetic hadeeth.”

After paying back the debts, the remainder of the inheritance shall be divided among the heirs according to the Shariah.

If the heirs are only the husband and the cousin from the father’s side, then the husband gets a half as his legal share due to the non-existence of direct heirs, as Allah says (what means): {And for you is half of what your wives leave if they have no child..} [Quran 4:12]

The remainder will be for the cousin from the father’s side by Ta’seeb (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); as the Prophet said, ''Give the prescribed share of inheritance to those who are eligible for it and the remainder [of it] is for the nearest male blood relative.” [Al-Bukhaari and Muslim]

Therefore, the inheritance should be divided into two shares, the husband gets one share, and the cousin from the father’s side gets one share.

Allah knows best.