The header on this page is made in Beaver Themer.  We could have used another method to replace the header such as:

 

The php below creates a shortcode of the Beaver Builder Theme search (which must be enabled in the customizer).

In this case I have added the shortcode [*bb_search] as a custom menu item and styled with the CSS below. You could add to a Beaver Builder HTML or TEXT Module.

* remove this from the shortcode. It is there to stop search showing here.

Beaver-Builder-Search-Icon

PHP

// Add this to function.php file in the Beaver Builder child theme

function bb_search_shortcode() {
 ob_start();
 FLTheme::nav_search();
 return ob_get_clean();
 }
 add_shortcode( 'bb_search','bb_search_shortcode' );




CSS

/* Positions the icon */ 
.fl-menu .fl-page-nav-search .fa-search { padding: 2px; }

/* Positions the drop-down form*/
.fl-menu .fl-page-nav-search FORM { margin-top: 20px; }
Beaver-Builder-Theme-functions.php
Custom-Link-in-Beaver-Builder-Menu

With the WordPress Search Widget

I bought the Pro package  a while back  as new modules, plugin and themes are getting added. The price is presently $99 for life updates. I suspect the price will increase as more is added.

 

I am still testing, but I'm very pleased with what I got (off canvas menu particularly more later).