That rather depends on your theme. what is happening, I suspect, is that the normal page is using theme template ‘A’, but when the search is done, it switches to search.php template. Instead, you need to figure what the real (in the theme) name of template ‘A’ is, and specify that in the S&F form settings.
However, you will then need to edit that template to add the results filter. It might be very easy, it might not. See this post for example, where this was done:
https://support.searchandfilter.com/forums/topic/help-with-search-form-creation/page/2/#post-65516
The key was the code:
$args['search_filter_id'] = 16439;
.
