I am aware of the obvious/sarcastic answer to my question. “Step 1: Take a picture of what’s behind monitor. Step 2: Apply it as desktop background.”
What I want to know is the specifics - specifically how to work out the positioning of the camera to ensure that what is seen on the desktop looks correct.
I suspect it’s something along these lines…
Take picture with camera on tripod and monitor removed.
Crop to the part of the picture that occupied the space where the monitor was (being careful to crop very precisely - perhaps using another picture taken from the same point but with the monitor still there as a reference for where to crop)
Apply the crop to the desktop.
Take another picture of monitor with desktop applied… from same point as before.
The last one is optional (if you want a picture of the acheived effect. You might just want to look at your monitor with its behind scene on its desktop)