Yes, OP is still around
), marvelling your prolific responses.
Thanks to you all!
It seems to me I might have caused some misconception using the word "desktop". I did NOT mean "virtual desktops" which most of the window managers support and between them windows can easily be moved by drag&drop. My scenario, however, is a combination of $DISPLAYs, one of them e.g. KDE at :0 and a vnc session running on :1. The "virtual desktop switcher" (kde4 plasmoid) handles virtual desktops, but not separate vnc displays, and the OP is not a Xinerama/TwinView thing.
Suppose you are working with thunderbird, lock your screen, move elsewhere, establish a ssh connection with a tunnel to your workstation where a vnc server is running, too, listening to some port at localhost only. You may now start a vnc session to your remote session and get an empty desktop (managed by the window manager you defined in .vnc/xstartup). Finally, you want to "pull" the window from one application :0 to :1, so to say.
Of course, when it comes to a mail client only, "killall thunderbird ; thunderbird" would be a simple solution, too. But what if the application you want to continue working with from the remote location (and maybe again locally, when you returned) could not be interrupted by kill without data loss?
The only workaround I know by now is working with a vncviewer even locally, and starting all applications you permanently need inside it.
But this is somewhat ill-favoured, there might be a smarter solution, too.