created_by_invite scope and test method checks invitation_created_at, because invitation_sent_at can be nil if skip_invitation is used

[skip CI]

In the latest version of Devise, they have made inheriting from a Devise controller keep the same I18n keys.
https://github.com/plataformatec/devise/pull/3407

I'm not sure if this is a breaking change, it wasn't for Devise (it would have broken our app though)

A lot of these bullet points could be paraphrased (better), but
this is at least a starting point.

[ci skip]

active_for_authentication? is only called if password is right, however
invited users has no password by default in devise_invitable, so it's
not used.

Override unauthenticated_message so a different message is displayed
when an invited user tries to sign in.