Grandchildren do not inherit from their grandfather if he has a son or sons still living
Question

My grandfather died before his father [my great-grandfather], and my grandfather’s sons, including my father and my paternal uncles, did not inherit anything from their grandfather. The sons of my great-grandfather inherited, and when we asked them to give us some of the inheritance, or we asked why we did not receive anything of the estate, they said: Your grandfather died before his father, therefore you do not inherit. Furthermore, they said that for us to inherit, all the sons of my great-grandfather must have died, but in fact they are still alive. My question is: is their argument sound? Is it true that we cannot inherit according to Islamic shari‘ah?
Praise be to Allah.One of the conditions of inheritance is that the designated heir must be alive after the death of the testator [the one who leaves an estate behind], hence your father and paternal uncles would have inherited from their father if he died during their lifetime and left wealth to be inherited.
But as the great-grandfather has died, his living heirs – who are his children – inherit from him, and the children of his deceased son cannot inherit, because they are prevented from doing so in this case.
The guideline is that in the case of inheritance, if there is a son or sons, and also grandsons, the grandsons are prevented from inheriting by the presence of their paternal uncles, and they do not inherit anything.
Based on that, what you were told is true, so there is no share of inheritance for your father and paternal uncles from your great-grandfather, so long as he has sons who are still alive.
Shaykh ‘Abdullah ibn Jibreen (may Allah preserve him) was asked: Can grandsons inherit from their grandfather, if their father died before their grandfather? If the answer is no, why is that?
He replied: In this context, grandsons refers to sons of sons, not sons of daughters. If their father dies before his father [their grandfather], they do not inherit from their grandfather if he leaves behind a son or sons, because the son is closer [to the deceased] then the son’s son. If the grandfather leaves behind no sons, not even one, and he only leaves behind daughters, then the grandsons receive what is left after the daughters are given their shares of inheritance. Similarly, the grandchildren may inherit from their grandfather, if he left behind no sons and no daughters, because they take the place of his own children, so each male will receive the share of two females."(Majallat al-Haras al-Watani (issue no. 264, 1/6/2004).
But these grandchildren may still receive something from their grandfather’s estate in two ways:
The first way is if the grandfather made a bequest to them before he died, bequeathing one third or less of his estate. He may do this if he has a great deal of wealth, and this bequest is obligatory to some of the scholars and recommended (mustahabb) according to many of them.
The evidence for that is the verse in which Allah, may He be exalted, says (interpretation of the meaning):
{Prescribed for you when death approaches [any] one of you if he leaves wealth [is that he should make] a bequest for the parents and near relatives according to what is acceptable - a duty upon the righteous} [al-Baqarah 2:180].
Shaykh Ibn ‘Uthaymin (may Allah have mercy on him) said: What we learn from this verse is that it is obligatory to make a bequest for parents and near relatives, for one who is leaving behind a lot of wealth, because Allah, may He be exalted, says: {Prescribed for you}. The scholars (may Allah have mercy on them) differed as to whether this was abrogated by the verses on inheritance or it is still applicable, as the verses on inheritance are more specific. There are two views, and most of the scholars are of the view that it is abrogated, but the more correct view is it has not been abrogated, because it may be understood as specifying. Hence it may be said that the words {for the parents and near relatives} apply specifically to cases where they have an allocated share, meaning that if they have an allocated share, no bequest can be made to them, because what Allah has allocated to them of inheritance is sufficient. Thus the verse remains general in meaning and refers to those other than the heirs who have been given allocated shares.
We also learn that it is permissible for the individual to make a bequest of whatever he wants, but this is restricted by the hadith of Sa‘d ibn Abi Waqqas (may Allah be pleased with him), according to which he said to the Prophet (blessings and peace of Allah be upon him): Can I give two thirds of my wealth [as a bequest]? He said: “No.” He said: One half? He said: “No.” He said: One third? He said: “One third, and one third is still a lot.” Agreed upon. Based on this, the bequest should not be greater than one third of the wealth, so the verse is restricted by the hadith.
We also learn that the obligation to make a bequest only applies in the case of one who is leaving behind a great deal of wealth, because Allah, may He be exalted, says: {if he leaves wealth}. As for one who is leaving behind a small amount of wealth, it is best for him not to make bequests if he has heirs, because the Prophet (blessings and peace of Allah be upon him) said to Sa‘d ibn Abi Waqqaas (may Allah be pleased with him): “If you leave your heirs independent of means, that is better than leaving them dependent and asking of people.” Agreed upon."(Tafsir Surat al-Baqarah 2/306).
The second way is for the paternal uncles to give them something of their shares of inheritance as a gift, to be distributed to them.
And Allah knows best.