On the non-CFW Switch, try to launch a game, and it'll ask for User. Rather than selecting an existing user, click on the (+).
At the next screen, where the options are Create New User and Import User from Another Nintendo Switch Console, opt the latter option.
With that, you can transfer over the user profile and the saves associated.
You could also try:
In System Settings > Data Management > Transfer your Save Data
to do save data transfers locally.
I've been using this to transfer my saves to and fro my CFW unit, so that I can back it up.
As I have the same profile on two Switches, I can connect to the same HOME app on either Switch