autofill form from another on my site

I have two forms my site, one on the homepage and one on the “search results page”

i am using a plugin to create the homepage form (wp custom fields search)

and the search results form is done by custom code,

what i need is,

for example a user enters “london” in location field on homepage, then hits search,
and then on the search results page the location field will automatically have “london” inputted,

is this possible?

thanks