Replacing Bathroom Vent Fan
It should be replaced with a modern exhaust fan. The roof vent should also have a cap or shield to keep water from leaking down the duct. I would recommend removing the entire exhaust system and start anew.
It will take less time than trying to adapt a fan motor to a outdated and unprotected roof vent than installing a new system. The roof is already opened as is the ceiling. You'll need to cut the drywall to accommodate the new fan box.
Installing a new duct to the roof and connecting it to a new roof vent  is not hard.