The reference to the Allies as the "United Nations" predates the picture. It was first used by Roosevelt on January 1, 1942 in a declaration titled "Joint Declaration of the United Nations on Cooperation for Victory"
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He moved to create a "grand alliance" against the Axis powers through "The Declaration of the United Nations," January 1, 1942, in which all nations fighting the Axis agreed not to make a separate peace and pledged themselves to a peacekeeping organization (now the United Nations) on victory.
http://www.fdrlibrary.marist.edu/fdrbio.html