I've been struggling with this too, and it seems like it's not possible to do this. The docs for https://core.telegram.org/api/links#message-links do say "private groups" at the top, which sounds like it should work. But if you look below where the parameters are defined, it says "Channel or supergroup ID." So I think it doesn't work with "non-super" groups.

Maybe you can solve your problem by forwarding messages? That's what I've been considering.