I don’t need that, thanks. What you want cannot, yet, be done, on the results page. We have received feature requests to allow the one form to be broken into parts to be placed (and styled) in different places (and differently styled) on the page.

We have taken those requests on board for our forthcoming V3 (which we hope to release in summer 2020 – but that may flex a little as we polish the code and UI). For example, you might have a form in WooCommerce that has a Search Box (text field), a Sort Order drop down, and then other fields (Product Categories, Product Tags, Variations, etc). You will be able to place the Search Box in the header, and the Sort Order above the products, and the rest of the form in the sidebar.

But, that is not possible right now.

As to taking a theme search (like one might see in a header or main menu) and directing that to our search form, this is possible, as long as, on the results page, the Search & Filter form also has a text search. Also, on the search results page, the two forms will NOT ‘talk’ to each other (see my earlier comments about splitting the form up).

Thanks for letting me know. I will close this thread for now.