This guide should be able to help on how to backup all you Fences layout: https://forums.stardock.com/486084/fences-support-faq#backupsnapshots. But, to make it work exactly the same on another computer. That new computer need to have the same files on your new system, specifically on your desktop folder and for all the Portal Fences, the linked folders need to be at the same physical location in the new system.
Easiest way, I believe, is to clone the old system Hard drive into the new one.
Stardock Community Assistant.