Can I copy a group in Sketch Up Pro into another Sketch Up Pro model?
Sure. Select it in the first window. Click Edit>Copy or use the appropriate keyboard shortcut. Go to the other window and click Edit.Paste or Edit>Paste in place if you want it in the same location relative to the model axes…
As Dave says. The only restriction would be if you were copying to another instance of Pro that was an earlier version…unusual, but not impossible. Even then, there are workarounds.