At first I was thinking of giving him my Ruger 10/22, but with its intricate method of locking the bolt back, the 10/22 is not very one-arm friendly.
I bought a 10/22 about forty years ago. (Ugh. Makes me feel old....) Took me about a week of using it, to decide to remove the bolt hold-open lever. Found it awkward to use, even with both hands, and it was causing a lot of issues, when shooting, as it seemed if you breathed in it's general direction, it would lock the action open. Never looked back!
Any time I have been at a range where they wanted the action left open, I stuffed a 12 gauge hull into the ejection port.
A lefty 10/22 action is available, I think, from a couple custom makers, if he is shooting off his left shoulder. Shooting off his right shoulder, the ejecting brass is not as much a thing...IIRC, at least one of the custom action makers had a Fortner style toggle lever operated 10/22 action available too. Dunno if it was available as a lefty, though.
Depending on what the style of shooting he enjoys is, a 10/22 may not be the best choice. Fun for shooting reactive targets, not so much for shooting groups, if ya know what I mean.
If he is more into accuracy than fast shooting, I would aim towards the available Anschutz single shots. The Model 64 was the basic model, the 54 Action was pretty much the 'best' action, the Fortner was designed for the Biathlon shooters, but is a pretty nice rig too (as it should be!). CIL sold a lot of Anschutz rifles rebranded with their markings, too.
Other accurate single shots to look at are guns like the BSA small Martini actions, as well as the BSA Martini Internationals of about any Mk. The Internationals were available handed, and eject the case with some enthusiasm, so which shoulder he shoots from would be worth noting.
Anyways, good luck in your search. Not a bunch of Lefty oriented semi's out there. My brother bought two of the Norinco Browning semi clones, back when SIR was still a thing, and they both were a little rough, but have been reliable shooters. One broke an extractor after several thousands of rounds, and got a genuine Browning part (as it was available) dropped in to it. The only other work done to either, was to round over the sharp edge of the chambers a wee bit, to rectify that edge, cutting slices off the side of the bullet, or jamming up on same when it cycled. Trouble free since.