How to change HTML generated by module
All modules generate their HTML through their own view files.
If you wish to override view file in folder: ip_cms/modules/administrator/search/view/search_box.php, you need to copy this serach_box.php file to directory: ip_themes/your_theme/modules/administrator/search/view/search_box.php and change required html parts.
NOTE: Don't modify original view files because they will be overwritten on update!
NOTE: This method also works on widget layouts.