Comment approval permission to non-admin user

I take that "moderator2" is a username name used for a user account. In that case, if you want to give to moderator2 the permission to administer comments, then you have to associate the user account with a role you only give to those users you want to be able to administer comments, then you visit the page on admin/user/permissions, and select "administer comments" for that role.

In this case, I called the role "comments moderator" but I could have chosen another name.

If "moderator2" is a role name, then on the page at admin/user/permissions you see something similar to what shown in the following screenshot.

The permission is the same as before.

P.S. The only permission for which you are interested is "administer comments." The other permissions don't influence that one, and users with a specific role would be able to approve comments, even without to have (for example) the permission to access comments.
The only permission associated with the page at admin/content/comment is "administer comments."

 $items['admin/content/comment'] = array( 'title' => 'Comments', 'description' => 'List and edit site comments and the comment moderation queue.', 'page callback' => 'comment_admin', 'access arguments' => array('administer comments'), 'file' => 'comment.admin.inc', );