Is it obligatory to return the inheritance taken by the deceased from his mother, considering his pledge to arrange for her Hajj, and does this affect the distribution of the estate among the heirs (3 sons, a daughter, and a wife)?

If the father took money from your mother that was her inheritance, then if it was a debt upon him, it must be returned from his estate before its division. However, if it was a gift conditioned upon Hajj or Umrah and he did not fulfill it, the money must be returned to her. But if it was an unconditional gift, then the money is not deducted from the estate.

And if the deceased left no heirs except a wife, sons, and a daughter, then the wife receives one-eighth due to the existence of a inheriting offspring, and the remainder goes to the children, with the male receiving the share of two females. The estate is divided into eight shares: one share for the wife, two shares for each son, and one share for the daughter.