Refresh Media Library after manual FTP upload?

I was just asked to help fix a WordPress site that had recently been migrated from one web hosting provider to another, and that was missing a lot of embedded images afterwards.

I learned that the person who originally migrated the site used the XML file export/import method .. which we suspect resulted in only a small percentage of the media library items having been migrated successfully (likely due to timeout or permissions issues).

So .. I managed to get into the old web hosting account and to zip up the "uploads" folder and download it, and -when I uploaded this folder to the new site (manually via FTP - to preserve the directory structure) -- lo and behold -- all of the embedded images that were previously missing started displaying.

However .. none of these newly uploaded/restored media items are showing up in the new media library. For example, I just uploaded something like 6000+ images .. yet only 893 of them are displaying in the new media library .. the same exact number of images that were showing up before I manually uploaded the 6000+ images.

What's the quickest, easiest (and safest) way that I can correct this problem?

Thanks!
- Yvan