update_menu_link_save.php

<?php
/**
 * Initialise a default menu entry
 * 
 * @see https://gist.github.com/dan-sprog/bd10acfbfed739e2d627
 */
function hook_update_N() {
  $t = get_t();
  if (!menu_link_get_preferred('path-here', 'menu-name')) {
    $item = array(
      'link_title' => $t('Back to case studies'),
      'link_path' => 'path-here',
      'menu_name' => 'menu-name',
    );
    menu_link_save($item);
  }
}