Is it permissible for my nephew to marry my female cousin, knowing that my nephew's grandfather and the girl's father are full brothers, and I am married to her sister? Is this marriage Islamically permissible?

Your nephew is permitted to marry that woman because she is his paternal uncle's daughter. A paternal uncle of the father is considered an uncle to him and to his descendants thereafter. Allah has made this lawful in His saying: "and daughters of your paternal uncles and daughters of your paternal aunts, and daughters of your maternal uncles and daughters of your maternal aunts."