Firstly: 

When a person dies, his estate is to be divided among his living heirs only. There is consensus on this point among the fuqaha’. Hence the scholars have stated that one of the conditions of inheritance is that the heir be alive after the person dies. 

See: al-Mawsoo’ah al-Fiqhiyyah (3/22). 

So the fourth son, who is deceased, has no share of the estate. 

His children do not inherit either, because the grandchildren do not inherit from their grandparents if any of their paternal uncles are alive, according to scholarly consensus. 

See: al-Mughni (9/22) and al-Tahqeeqaat al-Mardiyah fi’l-Mabaahith al-Fardiyah by Shaykh Saalih al-Fawzaan (p. 114-115). 

Based on this, the children of the son who died before his mother’s death do not get anything, because they are prevented from inheriting by the presence of their paternal uncles. The estate is to be divided among the living only, namely: the husband, the three sons and the daughter. The husband gets one-quarter because there are  descendents of the deceased, and the rest goes to the sons and daughter, with each male getting the share of two females. 

Secondly: 

It is mustahabb to give the children of the deceased son something of the estate, either as a bequest from their grandmother before she died, so long as it is not more than one-third, or by their uncles and aunt giving them something, so as to soften their hearts, especially if they are in need. 

In the answer to question no. [Ruling on the binding will (wasiyah wajibah)], we have stated that the law on the binding will (wasiyah wajibah) is invalid, and that wealth taken by means of it is haraam wealth. 

Thirdly: 

Our advice to the children of the deceased son is to fear Allaah and beware of consuming wealth unlawfully, because they have no right to this estate, as stated above. The Prophet (peace and blessings of Allaah be upon him) said: “It is not permissible to take the wealth of a Muslim unless he gives it willingly.” Narrated by Ahmad (20714) and classed as saheeh by al-Albaani in Saheeh al-Jaami’ (no. 7662). 

And he (peace and blessings of Allaah be upon him) said: “Every body that is nourished from haraam sources, the Fire is more fitting for it.” Narrated by al-Tabaraani and Abu Na’eem from Abu Bakr (may Allaah be pleased with him), and classed as saheeh by al-Albaani in Saheeh al-Jaami’ (no. 4519). 

They should understand that the ruling of the court is contrary to sharee’ah, and it is not permissible for them to take this money or for them to ask for it or to compete with the heirs for it. 

Our advice to the judges is to reject this law and disavow themselves of it, because it is a transgression and it is implies correcting the division of the estate that Allaah Himself has decreed.  

With regard to the heirs – the husband, sons and daughters – they should willingly donate some of the estate to the children of their deceased brother, so as to maintain ties of love among them and soften their hearts, especially if they are poor.  

We ask Allaah to help us all to do that which He loves and which pleases Him. 

And Allaah knows best.