How can I rehang heavy fire doors?
I see in your picture that there is a wooden shim between the door frame and the jack stud.  Typically the frame should be screwed into the jack stud separately from the door hinge.  The small door hinge screws should only have to hold onto the frame of the door and usually don't need to be driven into the wall stud.

A fire door can be quite heavy though and might need a bit more.



You can see here that they make door hinge hardware that comes with at least one extra long wood screw that will anchor your door hinge to both the door frame and the jack stud.  This will also further strengthen the door frame itself.

Go to the door accessory section of your local hardware store and find where they keep plastic packs of door hinge hardware.  Each hinge typically comes with short screws and one long screw.  Each pack is cheap, usually under $4, you will need three.  Make sure you match the shape and hole pattern of the existing door hinge.