Is the mother entitled to keep all the property inherited from her deceased father, or must the heirs of the heirs be informed and the inheritance divided among them? And is he who later inherits this inheritance sinful if the mother refuses to inform or bequeath them?

If the grandfather registered his property in the name of his daughter to be hers after his death, this is a bequest to an heir, and it is not effective unless the remaining heirs consent. Their mere silence is not considered consent. In this case, the property must be divided according to Islamic law among all heirs, and the share of any deceased heir passes to their own heirs. However, if the grandfather registered it in her name and transferred ownership to her during his lifetime, and the mother took possession of the gift and disposed of it as an owner, then this is a complete gift made during the lifetime of the donor and is not an inheritance.