Found the error myself and as it's only available in German I'll put the solution in here in English also:
change code in line 28 of include_searchform.
php to:
echo '<label for="mod_forum_search">Suchen : </label>'.
'<input type="text" id="mod_forum_search" name="mod_forum_search" value="';
if (isset($_REQUEST['mod_forum_search'])) echo htmlentities( htmlspecialchars( stripslashes($_REQUEST['mod_forum_search'])));
echo '" />';
And as a newbie I forgot to check the modules thread first...
The German one is here:
http://www.websitebaker2.org/forum/index.php/topic,15071.0.html