Moving sidebar links to below the header menu

I assume that this plugin adds a widget that you put in sidebar so edit your page.php and add a sidebar on the top where you can add this widget with those links.

register_sidebar(array(
  'name' => __( 'Phone Extra Info' ),
  'id' => 'phone-info-sidebar',
  'description' => __( 'Widgets in this area will be shown on top of a page' ),
));

of course you can add all the before and after widget arguments that the array takes. See the reference for more.

Reference:

• register_sidebar