All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
If the situation is as you mentioned in the question that the grandmother denies that your cousin suckled her milk, then there is nothing which implies the prohibition of your male cousin marrying his female cousin, and it is permissible, Allaah willing, for him to marry his cousin unless there is another impediment which prohibits their marriage.