How is the inheritance to be divided among the mentioned heirs, given that the deceased did not perform Hajj despite being able to, and no one performed it on his behalf?

If a woman who was able to perform Hajj dies without having performed it, her heirs must allocate the cost of Hajj from her estate before its distribution, as it is a debt that takes precedence over the rights of the heirs.

As for the distribution of the estate after deducting the cost of Hajj, it would be as follows: - The husband receives one-fourth due to the existence of a lineal descendant, based on the verse: ﴿But if they have a child, then for you is one fourth of what they leave, after any bequest they [may have] made or debt.﴾ [An-Nisa: 12]. - The father receives one-sixth due to the existence of a lineal descendant, based on the verse: ﴿And for his parents, to each one of them is a sixth of what he left if he had a child.﴾ [An-Nisa: 11]. - The remainder goes to the three sons by way of ta'sib (residuary heirship) equally, based on the Prophet's ﷺ saying: "Give the prescribed shares to those entitled to them; then whatever remains is for the nearest male heir."

Nothing goes to the rest of the heirs (such as the full siblings or paternal/maternal half-siblings) because they are excluded from inheritance due to the presence of the son and the father.

The estate is divided into 36 shares: - The father receives 6 shares (one-sixth). - The husband receives 9 shares (one-fourth). - Each son receives 7 shares.