So you want to share your clipboard across the machines? x2x is free software to do that over x server protocol.

1. Install x server and x2x on both machines. On windows/wsl use these instructions.

2. On remote system, if you use gdm, edit /etc/gdm3/custom.conf to add:
   

   [security]
   DisallowTCP=false
   

   and restart gdm sudo service gdm3 restart.

3. Find out on which display X server is running on remote machine.
   

   # on remote machine,
   $ echo $DISPLAY # This command assumes that you are logged in using some GUI method, vnc/rdp/nomachine etc.
   # Let's say it was 0.0
   

4. On local machine issue below command:
   

 # on local machine:

 $ ssh -XC remoteMachine x2x -east -to :0.0

References

1. Ubuntu wiki x2xHowTo