Is it legally true that the grandchildren of a deceased do not inherit from their grandfather if their father (the son of the deceased) died before his own father, and that their inheritance is conditioned upon the death of all the deceased's grandfather's children?

A condition for inheritance is the survival of the heir after the death of the deceased. If the grandfather's father dies and has living sons, they inherit from him, not the sons of his deceased son, because the sons block the grandsons (sons of the son). Therefore, your father and paternal uncles have no inheritance from your grandfather's father as long as he has sons.

Sheikh Ibn Jibreen stated that grandsons do not inherit from their grandfather if he has a living son (their paternal uncle), because the uncle is a closer relative. However, if the grandfather has no male offspring but only daughters, then the grandsons receive what remains after the daughters' share. They inherit from the grandfather if he has neither sons nor daughters.

Grandsons can obtain a portion of their grandfather's estate through two ways: 1. The grandfather bequeaths to them a third or less of his estate before his death, especially if he has considerable wealth, based on the verse: (Prescribed for you when death approaches any one of you, if he leaves behind good, is a will for the parents and near relatives with righteousness – a duty upon the righteous) [Quran 2:180]. Sheikh Ibn Uthaymeen clarified that this verse is not abrogated but rather specified, making a will obligatory for those who are not heirs. The bequest should not exceed one-third, and the obligatory will is for those who leave behind considerable wealth. 2. Their paternal uncles (a'mam) gift them something from their share.