Is it permissible to marry the sister of my foster nephew, and is she lawful for me?

If the girl was suckled by the milk of the man's brother, then she is forbidden to him, and it is not permissible for him to marry her; because he is a brother to her father through suckling, and "what is forbidden by lineage is also forbidden by suckling." However, if she was not suckled by the milk of his brother, but rather she was suckled with his brother's son by another milk, then there is no harm in marrying her, unless there is another reason for the prohibition.