ProMonitor runs under IIS, so the easiest way is probably to make both SSO via AD. That for you would involve putting your Linux server into the AD domain, and configuring an Apache plugin (see https://docs.moodle.org/28/en/NTLM_authentication )
Though it wouldn't surprise me if Compass Computer Consultants (the company behind ProMonitor) wrote a proper moodle integration eventually, or provided an SSO solution that didn't require system level integration, just app integration