moving a running client between two servers

[Gherald]

Is there any way to move a running client between two servers, or
between two different screens on the same server?  Using a proxy,
perhaps?

e.g. I have firefox or a terminal running on :0.0 and want to move it
to :0.1 or :1.0 or even otherbox:0.0 _without_ restarting it.

cloning would also be cool: showing the same window in two different
places, and accepting kb/mouse from both

-Gherald