Java - Perform a FTP command through a SSH tunnel

Question

I am developing a Java tool which uploads a file from one remote server to another.

The program will run on a laptop. The software needs to connect to serverA with SSH protocol then once it is connected to serverA, it has to transfer files to serverB through FTP. Files to be transfered are hosted on serverA.

I cannot directly connect to serverB because of a firewall.

Here is a summary:

Is it possible to do that with JSch? Something like the following:

JSch client = new JSch();
Session session = client.getSession("login", "serverA", 22);
// test purpose
session.setConfig("StrictHostKeyChecking", "no");
session.setPassword("password");
session.connect();
channel = (ChannelExec) session.openChannel("exec");
channel.setCommand("ftp -i ftp://username:password@serverB; put file.txt; close; quit;");

EDIT

What about writing a script and upload it on the serverA?

#!/bin/sh
ftp -n -i <<ENDOFINPUT
open serverB
user root password
cd /home/root
put xxx
close
bye
ENDOFINPUT