How to update/change anonymous author to authenticated current user upon logging in?
Try using the trigger 'after saving a new user account'.  You don't want to check for content every time they log in, just when they create an account that matches email addresses with those node.

For security purposes you should probably prevent people from being able to change their email address too or they might somehow steal someone else's content.

As for people who create content when they already have an account but are not logged in: create a rule that checks for accounts when a new node is saved.  So in summary:


New users should claim existing content when the 'after saving a new user account' is triggered.
New content by existing users (that are not logged in) should be automatically claimed by the user account upon saving the node.


Neither of these events require you to check when a user logs in.