How do I make an object appear on screen after it is collected?

In Unity you can layer up cameras at different depths and with different culling masks (the groups of objects that are visible to a camera).

By adding multiple cameras to your scene you can very easily have a FPS camera as well as an inventory camera that is drawn over the top.

Take a read of the Camera page from the manual: http://docs.unity3d.com/Manual/class-Camera.html

"You can create multiple Cameras and assign each one to a different Depth. Cameras are drawn from low Depth to high Depth. In other words, a Camera with a Depth of 2 will be drawn on top of a Camera with a depth of 1. You can adjust the values of the Normalized View Port Rectangle property to resize and position the Camera’s view onscreen. This can create multiple mini-views like missile cams, map views, rear-view mirrors, etc."

In your case I would move the letter cube to the inventory culling mask, parent it to the inventory camera and move it to an appropriate place in screen space.