Show menu items with limit access to anonymous users
Your problem is quite common.

Here is discussion how to implement such trick in Drupal 6 and 7 and 8: http://drupal.org/node/300607


  Drupal 6 (and 7) removed the ability to display menu items the user doesn't have access to. However, in some cases it is desirable to show a menu item even though the user doesn't have access to the menu item. For example, if you use an authentication mechanism that tries to acquire authentication when a 403 would be displayed, you still want to display the menu item so that users get a chance to provide credentials to log in.


Solution for Drupal 7 can be found here: http://drupal.org/node/300607#comment-4450062 

If you prefer ready module - you can download it here https://github.com/systemseed/always_visible