What is the ruling if one of my parental aunt’s sons has been requesting his dead mother’s share from my parental grandfather’s share taking into account that she had compromised her share?

Answer

Praise Be to Allah and Peace Be Upon His Messenger.

In fact, Allah, Himself, has taken the responsibility of distributing the shares fairly. He did not leave to humans or even prophets. To ensure fairness, he says: “There is a share for men and a share for women from what is left by parents and those nearest related whether the property is small or large-a legal share.” An-Nisa’: 7

Regarding, the woman’s compromise, it is not taken into account if she orally compromised. i.e., her action, in this regard, must be documented provided that she did not do that by force or a result of shyness. The rule says that whatever is taken because of shyness is considered haram (illegal), and the taker should not accept it. It is similar to wat is taken by force.  Both ways result in illegal properties.

Regarding the threatening claim that raising an issue to the court will lead to so many conflicts, I would say that this true. Nevertheless, all these conflicts are simpler than being in front of Allah on the Day of Judgement as He got angry with you because you took an illegal share. Allah says: “O you who believe! Eat not up your property among yourselves unjustly except it be a trade amongst you, by mutual consent. And do not kill yourselves (nor kill one another). Surely, Allah is Most Merciful to you.” An-Nisa’: 29

Allah also says after he had clarified the shares: “And whosoever disobeys Allah and His Messenger (Muhammad), and transgresses His limits, He will cast him into the Fire, to abide therein; and he shall have a disgraceful torment.” An-Nisa: 14

The prophet also said: “"Whoever usurps unlawfully even a hand span of land a collar measuring seven times (this) land will be placed around his neck on the Day of Resurrection". Related by Bukhari.

To finalize, I recommend that you resort to the Islamic Court and raise an issue. They can estimate the shares legally and solve the conflicts.