update current drupal user as ldap authentified

In my configuration I use the LDAP_FIRST_LDAP setting, and can log on to ldap using only the username. I have registered a user account with drupal, which at that time did not exist in LDAP. Later on, the same user name is added to the LDAP database (or the drupal user changes it's username to one also present in LDAP).
When logging on with the drupal password, he logs on as drupal user, when using the ldap user's password, he logs on to ldap but still has the properties as if he logged on as a drupal user.
What would be preferable is to update the user data as 'ldap_authentified'.
The _ldap_integration_ldap_login function could be modified as:

....
if( !$user->uid ) {
// new user
...
}
else {
// update current drupal user as ldap_authentified
$mail = $ldap->retrieveAttribute($dn, LDAP_EMAIL_ATTRIBUTE);
$user = user_save($user, array('name' => "$name$at$server", 'pass' => $pass, 'mail' => $mail, 'init' => $mail, 'status' => 1, "authname_ldap_integration" => "$name$at$server", 'roles' => array(_user_authenticated_id()), 'ldap_authentified' => TRUE, 'ldap_dn' => $dn));
watchdog('user', t('User %user is now ldap authentified.', array('%user' => theme('placeholder', $name .'@'. $server))), WATCHDOG_NOTICE, l(t('edit'), 'user/'. $user->uid .'/edit'));
}