Hi!
If the theme has a widgetized area in that location, you might be able to put it there without coding. Otherwise you might have to ask the theme author which PHP template file prints the header, and where exactly should it be the PHP search shortcode placed. Usually it’s the header.php file in the theme directory, but in some cases it could be different.
If he can’t help you, feel free to add temporary FTP and back-end details, and I will try to check it for you.