File references with absolute URLs

I'm redesigning a website for domain.com. The client wants to archive their current site, at archive.domain.com.

The current site was developed using an abandoned CMS (HotBanana) and is coded using all absolute URL references. Page request redirects I know how to handle, but what about for files (images, PDFs, etc.) that are used throughout the content.

Is there a way on the new site—which will be on a new/different server—to redirect these asset/file requests back to the original server where they exist?