Time to time I need to transfer site from server to server very quickly and have not common solution for this, because I have permissios.
Solution is to use http server if you have this one of server with backups or use netcat.
On server side I run
nc -l -p 8080 < mybackup.tar.gz
or
netcat -l -p 8080 < mybackup.tar.gz
and now can use wget, curl or browser for this url:
http://serveradress:8080
if you sent link to client it will best to do little more:
(echo -e "HTTP/1.1 200\nContent-Disposition: attachment, filename=mybackup.tar.gz\n
Content-Type: application/octet-stream\nConnection: close\n", cat mybackup.tar.gz )
| nc -vv -l -p 8080