Back to Search Page with Ajax Search Result

Hi staff,
first of all thanks for the greatest ajax plugin for search result!
I have a question.
I just customized search result template and use “Ajax – Result displayed on same page” option.

The site is this one: https://newsite.wildsicily.com/
When you search for a post type you can see my custom template. If you click on “Read More” button, the post will be show correctly.
If you push “go back” button of google chrome broswer or firefox, you’ll be redirect to the home page in the same div that I choose to show my results.

Does it possible to maintain the same results filterd like previuos research when I come back to previuos page?
If not, does it possible to redirect users (after they go back from browser) from the top of the previuos page instead into the div that I selected for the results?

I hope that the request is clear!
Thanks again for your great work!