Rule set username after changed user email I need an email registration system only in my drupal site.

I installed the module email_registration and I created a module like this http://www.grasmash.com/article/using-your-email-address-your-drupal-username to set the username like the own email address.

Now my user has: name: fra@ore.com email: fra@ore.com
But if the user changes is email address the username doesn't update. So if fra@ore.com changes his email to fra@ore2.com the username remain the same.

I tried to update the username by the Set a data value of Rules module After updating an existing profile but I dont know how set this action... Can you help me??
You can look at this: 
https://api.drupal.org/api/drupal/modules%21user%21user.module/function/user_save/7

It will run after a user is created and if a user is edited.   You can update the data as required.