Is it possible to add menu tab in any menu group?
Just change 

'type' =&gt; MENU_NORMAL_ITEM


to

'type' =&gt; MENU_LOCAL_TASK


and clear the caches.

The MENU_LOCAL_TASK option will make the menu item render as a tab in the user/% group. If you want to control the tab order you can use the 'weight' key in hook_menu().