How can I change sleep mode's wallpaper? I was able to change the wallpaper of the user accounts's window:



I did so by modifying /Library/Caches/com.apple.desktop.admin.png

But I also want to change the wallpaper of the sleep mode's window, which looks like so:



How can I do this?
Unfortunately what you are asking is not possible. Because the Sleep Mode just displays a blurred version of your desktop background, you cannot make it different than your desktop background.

You might try and find a script that changes your desktop background as soon as you sleep the computer and change it back as soon as you unlock it, but that would not be very feasible for everyday use.