Adding Login with Facebook button without using shortcode

I have noticed that when using default login forms or even login plugins, the "Login with Facebook" automatically appears when the option "Allow users to register with Facebook" is activated.

Now I have made a custom sidebar login widget via this awesome tutorial by Patrick Cohen:
https://premium.wpmudev.org/blog/wordpress-login-page-sidebar-login/

But this way the connect with facebook button doesnt show, obviously.
So my questions is how to ad one without using the shortcode. First, because it doesnt work inside the Shortcode Exec and second, when using the shortcode in the same widget it will result in 2 avatars and another logout link.

So how can I ad a "login with facebook" button (as an add on to the tutorial mentioned above) that will dissapear after being logged in?