Well since no one else has said, "32 S&W" is a caliber designation which applies to hundreds of different cheap low quality DA revolvers from the early 20th century. While it could easily be a S&W (will have barrel address on top behind front sight) odds are that it is not, because so many knock offs were made. Either way, it will be a family heirloom, and pursuing this legally is important.
Another consideration is possible antique status of the gun. We would need pictures, and a serial number (usually on butt of revolver or sometimes on the left grip frame, under the grip). You would have to check NJs laws for antique guns.
Winchester 73, the TFL user that won the west