I would not suggest placing your backup into public_html where the entire world could then retrieve it even if for a short time period. It is faster and easier to simply scp the backup to the new machine:
You'd replace $user with the cPanel username, destinationIP with the IP number for the new machine. After running the second command, you would be prompted for the password for the destination server.
scp /home/cpmove-$user.tar.gz root@destinationIP:/home/
Now, if you end up having SSH running on an alternate port on the destination machine rather than port 22, you'd simply add this section:
Replace port# with the alternate port on the destination machine.
scp -P port# /home/cpmove-$user.tar.gz root@destinationIP:/home/
If you have root user locked down where you cannot SSh as that user, simply scp to a sudo user's home that has shell access:
At that point, you'd replace sudousername with the sudo user that has shell access. This would save a copy of the cpmove-$user.tar.gz file to /home/subousername location. You'd then log into the destination machine, sudo su - to root and move the file from /home/sudousername to /home instead:
scp -P port# /home/cpmove-$user.tar.gz sudousername@destinationIP:./
After you have the account on the destination machine, then you can run "/scripts/restorepkg $user" at that point.
mv /home/sudousername/cpmove-$user.tar.gz /home