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.
The wealth that the deceased leaves is the right of his heirs. Abu Hurayrah narrated that the Prophet said: "Whoever leaves any wealth, it is for his heirs.” [Al-Bukhari and Muslim]
Each child of the deceased is entitled to his legal share according to the ruling of Allaah; Allaah says (what means): {…for the male, what is equal to the share of two females.}[Quran 4:11]
It is not permissible to reduce the legitimate share of any heir as this is injustice and transgressing the limits of Allaah. After Allaah mentioned the legal share of inheritance for each heir, He says (what means): {These are the limits [set by] Allaah, and whoever obeys Allaah and His Messenger will be admitted by Him to gardens [in Paradise] under which rivers flow, abiding eternally therein; and that is the great attainment. And whoever disobeys Allaah and His Messenger and transgresses His limits- He will put him into the Fire to abide eternally therein, and he will have a humiliating punishment.}[Quran 4:13-14]
Therefore, if your father had not been given his complete share, then he has the right to ask for what he did not receive from his share even if his mother is not pleased with it, but the matter should be kept hidden from the mother so as not to harm her. However, if your father decides not to ask for his share as a way of avoiding any problems and as a way of being dutiful to his mother and keeping good ties with his kinship, then this is good, and Allaah may give him something better than what he lost.
It should be mentioned that if a long period of time has passed since the time when the estate was divided, it may imply that your father has agreed to it. If this is the case, he has no right to ask for anything now.
Finally, you should be careful about the complexity of inheritance cases and the many claims that are made in this regard. They are issues that require much detail and information and the like, so it is better to take the matter to a Muslim judge or whoever is acting on his behalf in non-Muslim countries.
Allaah Knows best.