There is a manual online on this website available to subscribers, a small reasonable sized donation would be much appreciated

There should be no need for a jack.
It's simple, get someone to see if the cable moves at the carb end. One cable is accelorator, the other should be the choke.
I doubt the cable has broken, usually it is the small plastic clip that holds the cable onto the lever that snaps and the cable simply falls off the lever. Either this or it is carb side something has fallen off.
Hope it's carb side as lever side is a pain.
Good luck
