I can not change the author of the material, an error occurs. error code inside, along with a screenshot
The AJAX path used for autocompleting usernames (user/autocomplete) requires a user to have the access user profiles permission:

  $items['user/autocomplete'] = array(
    'title' =&gt; 'User autocomplete',
    'page callback' =&gt; 'user_autocomplete',
    'access callback' =&gt; 'user_access',
    'access arguments' =&gt; array('access user profiles'),
    'type' =&gt; MENU_CALLBACK,
    'file' =&gt; 'user.pages.inc',
  );


Make sure that is true for the user account that's entering the data into the autocomplete field. 

If the account does have the permission then the problem is specific to your environment (e.g. a module that alters access callback / access arguments of router item) and requires further debugging that falls out of the scope here.