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William Shakespeare first meet the second Phantom when he was a boy and then again on his many travels as a young man. He met the 2nd Phantom again when he stormed into the theatre when the 3rd Phantom was playing the role of Juliet in a play.
He once rescued the 2nd Phantom from death.
It makes sense that he would have connected the dots and is perhaps the reason why in both Lee Falk and Team Fantomen stories he tells the future 3rd to go to his father.