I found this but, it shows it for HB2 to HB3 camera/device transfers.
Don’t know if it will recognize HB3 to HB3 move.
Guess you’ll have to hook up the new home base and see if a transfer prompt shows up after a while.
https://support.eufy.com/s/article/How-to-switch-cameras-and-transfer-videos-from-eufy-Homebase-2-to-Homebase-3