No Windows 7 e superior, você pode fazer isso com o RDP padrão (Remote Desktop Client / mstsc.exe). Veja como:
/span for multiple monitors
If you pass /span to mstsc.exe, the target session’s desktop will
become a huge rectangle that equals to the summary area of your
physical monitors. This way the remote desktop window will fill all of
your screens. The downside of this approach is that both screens are
part of one desktop on the remote machine, so if you maximize a window
there, it will span all of your monitors. Also, a dialog that is
centered, will show up right on the border between your monitors.
There is software on the web to workaround that but I’m fine with
keeping my windows restored and sizing them myself. Also Tile
Vertically works just fine in this case.
Saving the /span option in the .rdp file
There is a hidden option that isn’t mentioned in the description of
the .rdp format:
span monitors:i:1
The screen mode is by default mode id:i:1
, which is windowed. To make if fullscreen set it to mode id:i:2
FONTE:
Você pode querer ver ISTO para mais explicações.