Is it permissible to marry the sister of one's brother through fosterage, when that sister is from his father by another mother?

Fosterage prohibits what is prohibited by lineage. So, if you were suckled by a woman, she becomes your mother. If your paternal cousin has a half-sister from his father's side, and his father's wife suckled you with his milk, she becomes your foster-sister, and it is impermissible to marry her.

However, if you were not suckled by her father's wife with his milk, and she was not suckled by your mother, and you did not share fosterage with her from another woman, then she is not forbidden to you. The mere fact that she is your brother's foster-sister does not make her forbidden to you. It is a condition for prohibitive fosterage to consist of five satiating sucklings.