The prohibition of marriage due to breastfeeding does not apply except after fulfilling the following:Firstly: It must be established. If there is any doubt, the breastfeeding is not taken into consideration, since the basic rule is the breastfeeding not taking place. It is not permissible to deviate from the basic rule except with a Shar`y (Islamically lawful) reason. Doubt does not prove it has taken place.Secondly: The number of times of breastfeeding must be 5 or more.Thirdly: The breastfeeding must take place during the first two years of the child's life.It is mentioned in your question that the girl's mother said that she had breastfed the man and then doubted doing it and the man's mother denies that this happened. If there is no one to affirm that the breastfeeding took place, the girl's mother's claim to have breastfed the man, though then doubting it after a while, has no effect on the validity of the man's marriage (Part No. 21; Page No. 133) to his cousin's daughter.May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.