Is it permissible for the the son of the son of the woman who breastfed the third brother to marry the fourth sister, given that the third brother was breastfed with the daughter of the third woman?

There is no objection to the aforementioned individual marrying the questioner's sister, as there is no Mahramiyyah (prohibition of marriage due to kinship) between him and her. The prohibition by fosterage occurred between his foster brother and whoever shared in the fosterage from the milk of the wet nurse. As for the rest of his siblings, there is no such prohibition. Therefore, her sister is not his paternal aunt, and he is permitted to marry her.