What kind of gear shifter is this? Single lever
I'd call it a thumb shiifter.   Guess its for the front derailleur, and on a bike that old its probably not indexed, which makes this easier.

Firstly is the gear wire loose?  Check them down on the frame and see if they're slack.  If so, the wire has snapped or the end has come off inside the shifter.

If you can't physically move the shifter then it could be jammed with wire or the "barrel", or just plain rusted.

That plastic bit on top is a handle- its the top of the tension screw.  If you undo it completely you'll be able to see into the mechanism for rust.  This is also how you'd get access to the cable to replace it.  Note your other-hand shifter is more likely to be indexed (ie click-stops at every gear position) so not directly comparable.

If the problem is rust, tell your friend to stop storing the bike outside.
If its a broken cable, that's a fairly straightforward fix, albeit dirty.