Is it permissible for my friend to marry her maternal cousin, given that her mother and maternal aunts claim that her grandmother breastfed him, while the grandmother denies this and does not remember the number of sucklings for any of them?

The prohibition of marriage due to suckling is not established merely by the testimony that "this is the son of this woman through suckling," because people differ concerning what constitutes prohibitive suckling. The witness must clarify the nature of the suckling, such as the number of sucklings and when they occurred. Accordingly, the man is not considered your friend's maternal uncle, and the marriage of a woman to her maternal uncle's son is not prohibited, although it is preferable to avoid such a marriage due to scholarly disagreement on the matter.