This module is working only for admin

can i safely assume that you are using the link 'invite/add' to call the add invite form since i am facing the same issue.

$items['invite/add'] = array(
    'title' => 'Add Invite',
    'page callback' => 'invite_admin_add_page',
    'access arguments' => array('create invites'),
    'file' => 'includes/invite.admin.inc',
    'type' => MENU_LOCAL_ACTION,
    'tab_parent' => 'invite',
    'tab_root' => 'invite',
);

Looking at the code i saw that the access callback attribute was not specified for the link. is this a feature or a bug?

If you omit "access callback", the callback function defaults to "user_access", which checks for the permissions listed in "access arguments".

Has your user been granted the "create invites" permission?

This is not a bug of the module. You should configure your permissions.