Hotkey to Move Window to Other Monitor
On my Linux Mint 17.2 Cinnamon edition are predefined shortcuts Super+Shift+Left/Right/Up/Down Arrow. They move active window to screen on left, right, above, below (depending on the arrow key). It works even on fullscreen windows.
With Gnome 3, you can use Super+Shift+Arrow.
It might work under Cinnamon, since it is based on Gnome 3.