moving photos to a new computer

If you have used the Organizer to catalog and tag your photos, you should not follow John's suggestion of simply copying the photos from your old computer to your new one.  You would lose a lot of information from your catalog.  Your best alternative is to create a backup of your Elements 13 catalog on your old machine and then use Elements 2020 to restore it to the new one.  During the restore process, the old catalog will be automatically converted to the format for Elements 2020.  If you have a large number of photo files, you may need an external drive to backup the catalog.  A USB flash drive may not be sufficient if you have a large catalog.

For more information about backing up and restoring your catalog, see the article in Nancy's post.

1. I have moved this question to Photoshop Elements for you.

2. Please see this help article on moving your Elements Organizer Catalog.

https://helpx.adobe.com/photoshop-elements/kb/backup-restore-move-catalog-photoshop.html

Plug your USB flash drive into the old computer and copy the pictures TO the flash drive

Plug your USB flash drive into the new computer and copy the pictures FROM the flash drive