Is it possible to directly transfer files between two remote servers when they don't use the same protocol? I have a lot of files on serverA (which, at least for now, must be accessed using SFTP) and want to copy them to serverB (which must be accessed using FTP). Unfortunately, I can't do anything on the servers themselves as I am an external client for both.
If I understand what you're asking correctly, I think you can do it with
sudo apt-get install sshfs
mkdir serverAFiles sshfs serverA:/path/to/the/directory serverAfiles
Now you will see the files on serverA in the 'serverAfiles' directory just as if they were on the local machine, and can ftp them onto serverB just as if they were local.
When you're done,
fusermount -u serverAfiles
will break the ssh connection and you'll no longer see the remote files as being local.