Is it permissible for the children of a deceased son to inherit from their paternal grandfather and grandmother? And is it permissible for a mother to write an apartment in her son's name without her daughters, on condition that he pays them an amount corresponding to their share after her death with their consent, or must she sell it to him for a small price, and do they still have a right in it? And is it permissible for her to gift him this apartment?

The son of the son and the daughter of the son do not inherit in the presence of a direct son. If registering the apartment in the name of one of the sons means that he takes it after her death, then it is a bequest to an heir, which is not effective unless the other heirs consent. If the intention was to gift it during her lifetime, then it is not permissible to prefer one son over others in giving, rather, justice must be observed between them. So, if the mother singles out her son with an apartment, she has sinned and is obligated to equalize, either by returning what was favored to some, or by completing the share of the others. An unjust gift is void and must be returned even after death.