You can display search form in the header of site only on mobile devices and not on desktop systems then you can achieve this by enabling the plugin option “Display search form in header on mobile devices” in the plugin settings page as displayed below.
Please note that the above displayed plugin option “Display search form in header on mobile devices” also hides the search form from the menu on mobile devices and this option sometimes does not work properly if your site uses any type of caching.
If your site uses any type of cache or if you want to also display search form in mobile menu then please also enable the plugin option “This site uses cache” as shown below but please note that it will also display search form in the site header on desktop that you can hide developing and using custom CSS code on your site.