This depends on when in the story you are asking about. The portrait hanging in front of the inn changes between the time that Rip goes to sleep and time that he wakes up again twenty years later.
When Rip goes to sleep, the Revolutionary War has not started yet. At that point, the portrait is the portrait of King George III of England. But by the time that Rip wakes back up again, the Revolutionary War has ended and the US is a free country. At this point, the sign in front of the inn has changed. Now it is supposed to be a picture of George Washington instead of the King.
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