If I were asking the question of the original poster, and if I were feeling a little bold, I would create a file called:
Navigate to the directory:
You *_may_* have to sudo nano or open nano as root. Nonetheless, whatever you have to do in that regard, while you are in the appropriate directory, run the command:
which will open a file using the nano text editor with the file name indicated.
Then, having at hand your path to desired login screen background image, just enter that path in the top line, or the second line (with a comment above it using a "#" at the beginning of the line to mark the comment). Then press CTRL-X, and the editor will ask you if you want to save the file with the name you opened it with, just press Enter a couple of times and log out, or reboot (I would probably reboot), then see what shows up after the reboot to check for success. That's what I would do, if I were in your circumstances.