Great!

After a couple of configuration problems, now it works like a charme!

To use Live (Microsoft) login enabled you have to add redirect urls within the Microsoft Application Registration Portal. Use these one to make it work:
https://[your_wp_domain]/wp-content/plugins/wordpress-social-login/hybridauth/endpoints/live.php

Otherwise a great tool, thank you!