Is the mother's verbal waiver of one-sixth of the inheritance to her deceased son's children, with witnesses present, considered legitimate and binding on the children, or does it revert to the deceased mother's property? And is it necessary to take legal action in this case?

The mother's share of her son's inheritance, which is one-sixth, goes to those to whom she relinquished it if they acquired possession of it before her death. This is considered a gift and is subject to the conditions of a gift. As for the wealth the mother leaves behind, it belongs to her heirs. Similarly, if those to whom the one-sixth was gifted did not acquire possession of it before her death, it is added to her estate and distributed among all her heirs, based on what Abu Bakr said to Aisha - may Allah be pleased with them both -: "O my daughter, I had gifted you twenty wasqs of dates. If you had harvested them and taken possession of them, they would have been yours. But today, it is the property of the heir, so divide it according to the Book of Allah."