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// ADD TOOLBAR MENU ITEMS //
function add_scree_toolbar($admin_bar){
  $menuName = 'You Menu Name';
  $screeMenu = wp_get_nav_menu_items($menuName);

  $admin_bar->add_menu(array(
    'id'    => 'parent-item',
    'title' => 'Menu',
    'href'  => '#',
    'meta'  => array(
        'title' => __('Menu')
    )
  ));

  foreach ($screeMenu as $menuItem) {
      $menuArgs = array(
        'id'    => $menuItem->ID,
        'title' => $menuItem->title,
        'href'  => $menuItem->url,
        'parent' => 'ai-item',
        'meta'  => array(
            'title' => __($menuItem->title)
        )
    );
    $admin_bar->add_menu($menuArgs);
  }
}
add_action('admin_bar_menu', 'add_scree_toolbar', 100);