by Paul Raper.
One approach that you might think about is LTI. LTI does require that both sides/applications use it, but it does provide a way for users to login to one application, and then transfer over to the other one.
It may be that someone else has another idea.
By the way, did you take a look at: https://docs.moodle.org/36/en/CAS_server_(SSO)_authentication