Should the deceased's will be carried out regarding a third for his sisters, a third for his sister's husband, settling his debt from the (remaining) third, and purchasing Qur'ans with the remainder, given that he left behind a mother, a brother, and three sisters, and has no children?

The brother's will cannot be fully executed, because the division of inheritance is from Allah. He is only permitted to bequeath one-third of his wealth to non-heirs. Anything exceeding one-third is contingent upon the approval of the adult heirs. Debts are to be paid from the principal of the wealth before the will and the division of the inheritance.

In the presence of full sisters:

The mother receives one-sixth. The remainder goes to the full sisters and the brother, with the male receiving the share of two females. No bequest is permissible to them because they are heirs, unless with the consent of the heirs.

In the presence of maternal half-sisters:

The mother receives one-sixth. The maternal half-sisters receive one-third. The remainder goes to the full brother by ta'sib (residuary heirship).

In the presence of paternal half-sisters:

The mother receives one-sixth. The remainder goes to the full brother by ta'sib. The paternal half-sisters do not inherit, and a bequest to them is valid.

Division of the one-third bequest:

If the sisters are heirs: The one-third is divided between the elder sister's husband and for purchasing Qur'ans. If the paternal half-sisters (non-heirs) are present: The one-third is divided into three equal parts: one-third for the paternal half-sisters, one-third for the elder sister's husband, and one-third for purchasing Qur'ans.

Inheritance of a divorced wife:

If the divorce was irrevocable (three pronouncements or khul') or her 'iddah (waiting period) ended before his death, she does not inherit. If the divorce was revocable and he died before her 'iddah expired, she inherits one-fourth (if he has no child).

It is advised to consult with scholars directly for a detailed explanation of the matter according to the specific circumstances.