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That's interesting you mentioned it. I heard of a man who had his forearm amputated. He mentioned how he can still feel sensations in what would be his arm. Whenever his 'arm' itches, he scratches his stub and the itch feels scratched.

Perhaps the sensory neurons at the elbow transform into arm sensors...

Though, this still wouldn't explain why he feels itching where his arm used to be rather than a part of his actual body...