Is waiving statutory shares of inheritance for some heirs, but not others, Islamically permissible, and is what devolves to those for whom the waiver was made lawful or unlawful? And if unlawful, what is the solution?

Scholars have differed on the ruling regarding favoring some children over others in giving gifts. The preponderant opinion is that it is not permissible, based on the hadith: "Be equitable among your children in giving gifts. If I were to prefer anyone, I would have preferred women." Therefore, your grandmother should not allocate her share of her husband's inheritance to her son exclusively, to the exclusion of her daughters, unless there is a valid Shariah-compliant reason, such as a large number of dependents. If that is the case, then it is permissible. Likewise, if her action was based on imitating those who say that equality is not obligatory, and the time for rectification has passed, then it stands and is permissible. Otherwise, you must return it and divide it among all her children (males and females) equally or with the male receiving the share of two females.

As for her waiving her share of her son's inheritance and gifting it to some of her grandchildren, there is no religious impediment to that, although equality among them is preferable. The correct view is that equality among grandchildren is not obligatory, as stated by Al-Mardawi Al-Hanbali, quoting Al-Harithi: "Not the child of his sons and daughters," and Ibn Qudamah's statement: "And he is not obligated to be equitable among his other relatives." Therefore, what the grandmother gifted to some of her grandchildren is permissible for them.