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Holding down desk top then clicking short cuts brings up a very limited list of apps (not the full list of apps on the phone). How do you put any app on the desk top?
Click the Apps at the bottom of your screen, find the App that you want to add to your Home screen, put your finger on it for a second or so and without taking your finger off it move your finger. This will open your Home screen and you can place the App wherever you want to on your Home screen. You can then reposition it at anytime by keeping your finger on it, or start another Pane (page) by moving it to one side of the screen.
From the home screen (or desktop as you've put) open the app drawer (tap on the white circle icon with 6 dots).
Then hold down on any app in the drawer and depending on your settings you either then drag it to the top of the screen onto where it says 'Add to home screen' and release, or otherwise holding the app down will take you to the home screen (desktop as you've put) where again you can drop it. To move it to other home screens simply hold down on it again and move to the edge of the screen depending on which direction you want to move it to.