This is what the concept of a homography was invented for. You know the coordinates of the four corners on your screen and on the wall, and you want to find a transformation that maps from screen coordinates to wall coordinates. There will be a homography that maps between the two coordinate systems. So, your task is: given four points with known mappings, find a homography that is consistent with that.

If you're using OpenCV, see the findHomography() method.

This is what the concept of a homography was invented for. You know the coordinates of the four corners on your screen and on the wall, and you want to find a transformation that maps from screen coordinates to wall coordinates. There will be a homography that maps between the two coordinate systems. So, your task is: given four points with known mappings, find a homography that is consistent with that.

If you're using OpenCV, see the findHomography() method, as well as warpPerspective().