Hi Djohan,
As per our understanding, please feel free to correct - Your existing users are stored in an external database and you want users to authenticate into both applications using the same credentials.
So miniOrange offers a perfect SSO solution for Moodle LMS according to your requirement,
You could simply connect miniOrange IDP with your External database , and configure Moodle as a service provider, enabling you to login into Moodle with the credentials of your academic system and setting up SSO for both the applications.
We would like to understand further more details about your academic system and would be happy to help and provide you with the required assistance.
If you need any more details please feel free to contact us at : info@xecurify.com