you can read about this here: https://forum.inaturalist.org/t/how-to-use-inaturalists-search-urls-wiki-part-2/18792#heading--annotations.
that said, the Identify screen will set the appropriate URL parameters based on your filter selections on that screen, and it passes these to the URL of the export screen. it just doesn’t pass it down to that gray box in section 1 of the export screen. so you can just copy from the URL and paste to the gray box.