This article explains how to replace the native search bars in the WoodMart theme by xtemos.
Step 1: Go to HTML Blocks -> Add New. Create block AJAX Search and add there a shortcode:
Step 2: Go to WoodMart -> Header builder and edit the header.
Step 3: Remove default search
Step 4: Add new element
Step 5: Select HTML Block
Step 6: Select AJAX Search block created in step 1.
The header with replaced search.