Yes, take the stirrups down a hole or two... also, try to do things to help him build a seat. For example, have him two-point at the walk, then try posting at the walk, before he trots. Bareback riding can also help.
If I were you, I'd take off those reins and just lunge the horse. Have him put his arms out, touch the ears, tail, touch his toes, etc. Stuff to build his confidence and teach him to rely on his seat instead of the reins. I ruined my first pony's mouth balancnig myself on it and wish I'd known better.
Oh, and since he has the opportunity, he might feel more comfortable with the horse if you do a bit of groundwork first :)
Good luck! At least your boyfriend is interested in horses. None of the guys I know will touch one with a 10-foot pole xD