Author can only see own post comment and can moderate

The default author role does not have the moderate_comments capabilities so you need to add that capability to the author role, so add this to your plugin:

function add_theme_caps() {
        $role = get_role( 'author' ); // gets the author role
        $role->add_cap( 'moderate_comments' ); // would allow the author to moderate comments
}
add_action( 'admin_init', 'add_theme_caps');