I'd say it depends on the games he plays. One simple test: run the game at low settings 1080p and note the framerate. Now run the same game the same way except lower the resolution to 720p and note the framerate.
If the framerate is a lot higher at 720p, this means he could use a better videocard for THIS game. He'd have to repeat the test for each game. The higher the framerate jumps, the more videocard he can use.
If the framerate doesn't increase all that much, it means a better videocard won't help that much in that game.
Personally, I wouldn't upgrade the card on this system. The reason is if/when he builds a new system there will be better cards to choose from. On the other hand, if he buys a 1060 3gb, which is the most I'd consider for this computer, then he's overpaying due to the current inflated prices.
I don't like the idea of buying a 1050 Ti due to their high cost yet they don't get you out of budget level performance. A regular 1050 is not enough of a jump to be worthwhile.