Hi @moises8,
Thank you so much for getting in touch, we really appreciate your time.
Unfortuantely, this is not presently supported by default and would require quite a fair amount of customization to achieve.
You will likely want to create this new search field on the page this is needed, and upon clicking the search button, submit this bypassing the search term as a GET variable which then once the user arrives and the map page, you should be able to then, using some more script grab that searched term via the GET variable and input this in the search field of the map, triggering a click during this time.
This should replicate the desired result mentioned.
I hope this helps?
Kindest Regards,
Steven De Beer