If you can provide the image, my random screensaver hack might help. It displays images on sleep/poweroff.
If you wish to preserve actual screen content, you'd need to adapt this hack a little (take a screenshot and then display the screenshot you took).
If you're looking for unconventional solutions, open up the device and disconnect the battery and whatever is on screen will stay there until you put the battery back in. Note I actually managed to break apart a battery connector this way...
Last edited by frostschutz; 03-27-2016 at 01:43 PM.
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