This isn't really "programming" howto, but heregoes.
Firstly, root login via ftp is (and should always be) disabled by default on linux servers, so this isn't something that should be done by any means. There are alternate ways of doing this, such as rsync. To rsync from server1 /backup to server2 /backup, the command is pretty straightforward. This shell script should get it done for you.
rsync $RSYNCARGS -e $RSYNCCMD $MYBACKUP:/$MYBDEST/ $MYBDIR
Depending upon the size of the directory, this will take a bit of time. Personally, I do this over ssh, you can do it without it, but I use ssh myself to do this.