You can set the background to black already and see if it changes. In fact this was written:
"We also measured how the content displayed on the
LCD affected its power consumption: 33.1 mW for a
completely white screen, and 74.2 mW for a a black
screen. Display content can therefore affect overall
power consumption by up to 43 mW"
http://www.nicta.com.au/pub-download/full/3587/
As such your claim is false for the model given in the paper. Don't fall for those wallpaper sites and they are a fine source of smart phone malware.
Bob
I was wondering if this is true? my cousin told me that he had his wallpaper on his smartphone replaced by a completely black wallpaper because it would save him a lot of battery. i'm wondering if its true? if i upload one like thesethese: Black wallpapers for android on my samsung Galaxy S6, will it really save me battery? i find it hard to compare, since you would need to measure the battery life in exactly the same conditions, but i find this very hard to do.... anyone who has a good technical explication for this if its true or not?

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