The incompetent buildings dept here in New York City after 5
inspections finally saw the vent and determined that the pipe he
installed, the tearing into the walls and the range hood he installed
did not require a permit, they also say that the 4" vent he has in the
shared soffit is not illegal. The ******* is uncooperative in
redirecting the vent because it might cost him $5.00 to do so.

Do you think it would be a viable solution to open up the soffit and
block off the area between the houses. Another idea I had was to
install my own rooftop vent to direct the fumes out of the soffit,
then sue him to cure this condition he created.