Is there a sin upon the mother who authorized her brother's wife to donate some of her deceased mother's belongings, based on her mother's will?

Scholars have differed on the permissibility of a guardian delegating their guardianship to another, and the preponderant opinion is that they are allowed to do so. As for the grandmother's silence, it is not considered permission unless there are indications that point to her consent. If the charity reaches its rightful recipients, then nothing is incumbent upon the mother; but if it does not, then the mother is responsible for guaranteeing it with its like or its value.