My brother wants to marry my sister through fosterage. Is that permissible?

Fosterage establishes the same prohibitions (mahramiyyah) as lineage. Thus, what is prohibited by lineage is also prohibited by fosterage. Whoever is nursed by a woman becomes her child and the child of her husband, the owner of the milk. This applies solely to the nursed individual, not to their siblings. Based on this, if there is no proven suckling relationship between the girl and your brother, she is a stranger (non-mahram) to him, and it is permissible for him to marry her. The fact that she is your foster sister does not make her prohibited for your brother.