Is it permissible to marry a girl whose mother is the sister of my older paternal brother through breastfeeding, given that my father's wife does not remember whether she breastfed me or not, knowing that she remembers breastfeeding my older sister?

If the girl's mother was suckled by the milk of your brother's mother, milk that resulted from your father's intercourse, then it is not permissible for you to marry her daughter, because she becomes like your sister's daughter. However, if she was suckled by milk not from your father, then she is a sister to your brother alone. Doubt about suckling has no effect, as the default is the absence of prohibition.