Is it permissible for a mother to keep her deceased husband's end-of-service gratuity for her daughter, to the exclusion of her two sons, knowing that he spent most of his money on the sons' education and that the remaining amount is much less than what was spent on them?

Tuition fees fall under the category of providing for children, and they vary according to need. If the two sons require university education while their sister does not, there is no injustice to her. The mother may suggest the idea of them relinquishing their share to their sister; if they agree, there is no harm in it.