oAuth2 + PHP-auth implementation

Well, I know how to implement oAuth2, but how to pair it with PHP-auth?

Example:

1. User goes to domain.tld/register
2. User choose Github as registration method
3. oAuth2 lib used
4. User goes to domain.tld/login
5. User choose Github as login method

Now, how to actually "login" user via PHP-auth? Because main authorization library would be still PHP-auth. Is it possible to programatically "login" user?

The issue names no files, tests, or entry points. Start by locating the PHP-Auth login and registration APIs and reviewing the described OAuth2 flow; done would require a documented, supported way to connect the external identity to PHP-Auth.

Written by the indexing model from the issue text.