Are you a cfi? You don't have to be but if you are you'll probably know how to keep records. I had to do this and I just signed his logbook each flight. I kept a detail of what we did. If he has no jet time he's going to bust the speed restrictions, suck at SIDS and stars, not know how to do a crossing restriction, and be behind in general. Probably. Realize when he busts a FAR or balls one up the Feds will call you which is why I said keep good records. If you can show what you instructed on and you covered whatever he messed up then you're far ahead of the game.
Hopefully your guy has a ton of kingair experience and this is his first jet. Good luck.