We want to access a computer inside a network without accessing the gateway server every time. In order to do that, we establish a tunnel between port 5555 in our computer (any port > 1024 would do), and port 22 of the target computer.
host.outside$ ssh -f -X me@public_computer.domain1 -N -L 5555:network_computer.domain2:22
# enter password
host.outside$
# copy file from computer2:/home/me/whatever/file_to_tranfer.tgz to host.outside:/whatever/you/want
host.outside$ scp -P 5555 me@localhost:/home/me/whatever/file_to_tranfer.tgz /whatever/you/want
# enter password again
Copy the public key in .ssh/id_rsa.pub from your computer to .ssh/authorized_keys in the target.
As explained here, when an SSH connection is idle for quite some time, it is usual to find the session frozen and/or closed with one infamous messages like Write failed: Broken pipe
or Connection to localhost closed. To solve that, modify .ssh/config adding this line:
Host *
ServerAliveInterval 60