I've found the solution by myself. The reaction time to forum posts is really too slow!

md_megamenu/templates/admin/megamenu_item_admin.tpl.php
Add the bold lines to the section of the 'a' type

<?php elseif ($type == 'a'):?>
  <div class="md-bl ei-link ui-draggable ei-processed" data-title="Add a link" >
    <input class="setting" type="hidden" autocomplete="off" value="type=a&a_title=<?php print urldecode($item->a_title); ?>&a_path=<?php print $item->a_path; ?>&a_target=<?php print $item->a_target; ?>&a_icon=<?php print $item->a_icon; ?>&class=<?php print $item->class; ?>">
    <a class="handle">+</a>
    <span class="ei-label">[link]</span>
    <span class="ei-text">
    <span><?php print urldecode($item->a_title); ?></span>
    </span>
    <a class="ei-remove" href="#"></a>
    <a class="ei-edit" href="#"></a>
  </div>

md_megamenu/templates/admin/menu_links_edit_form.tpl.php
Add the bold lines to the section of the 'a' type

<div data-title="Add a link" class="md-bl ei-link">
  <input type="hidden" autocomplete="off" class="setting" />
  <a class="handle">+</a><span class="ei-label">[link]</span>
  <span class="ei-text"><span></span> </span>
  <a href="#" class="ei-remove"></a>
  <a href="#" class="ei-edit"></a>
</div>

Regards,
Oliver