A person wants to marry his cousin, but her brother and his sister are siblings by breastfeeding. This person and the girl he wants to marry are not siblings by breastfeeding; that is,
the girl was not breast-fed by his mother and he was not breast-fed by her mother.
If the reality is as you mentioned, it is permissible for this person to marry his cousin, because the fact that his sister and her brother are siblings by breastfeeding does not have any effect on the lawfulness of their marriage. (Part No. 21; Page No. 75) May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.