Preview a post that uses a custom theme

I created a website for a client some time ago and it has just come to my attention that they are unable to preview blog posts accurately due to the standard way WP works. Blog posts are previewed using a default blog post theme. The client would like her previews to appear as they do on the website using the custom archive templates I have created. Is this possible? Can I amend the code the Preview button uses to display previews or is their a simpler work around?

An example of how the theme displays blog posts in a custom archive can be seen here: https://www.gsp-uk.com/?cat=5