I am using a MBP with OSX El Capitan. If I need to move a window from one Desktop space to another desktop space, I just need to hold the title bar and press Ctrl + 2 to move the selected window to Desktop space 2. For presentation purpose, I would like to have several desktop ready with the applications and then show respective Desktop space on external monitor/projector. Is there any shortcut key or Automator script, which can do this? In the mission control, I have setting checked "Display have separate Spaces", so I am not able to move the Application from one display to another display.
Not exactly what you're looking for, but I believe "Desktop 1" is the default for external displays. Any additional spaces on external displays get appended to the end of the spaces list.
It may be useful to "reserve" Desktop 1 for your presentation space.
To change this up — for example, if you want the monitor on the right to be your primary display — got to System Preferences > Displays > Arrangement. This window will show you the layout and relative resolution of all monitors currently connected to your Mac with each monitor represented by a blue rectangle icon.
One of the display icons will have a white bar at the top, representing the menu bar. To set the monitor on the right as the primary display, click and hold on the white bar at the top of the right icon and drag and drop it on the left icon.
That's it you're done...... Tell if this helps you.