So you want to share your clipboard across the machines?
x2x is free software to do that over x server protocol.
Install x server and x2x on both machines. On windows/wsl use these instructions.
On remote system, if you use gdm, edit
and restart gdm
sudo service gdm3 restart.
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
On local machine issue below command:
# on local machine: $ ssh -XC remoteMachine x2x -east -to :0.0