Researchers at The National Museum of Computing at Bletchley Park saw a "telegram machine" for sale on the auction site for £9.50 (12.5 euros/$14), and believed it may have actually been a Lorenz machine, used by the German army to send top-secret coded messages.
The museum is now hunting for a replacement motor, which is missing.
"It looks like an electric motor in black casing with two shafts on each side, which drive the gears of the Lorenz machine," said Wetter.
The Lorenz teleprinter was used in World War II to swap personal messages between Hitler and his generals.
A linked cipher machine consisting of 12 individual wheels each containing multiple settings encoded the messages.
Andy Clark, chairman of the trustees at The National Museum of Computing, called the machine "far bigger than the famous portable Enigma machine".
"Everybody knows about Enigma, but the Lorenz machine was used for strategic communications," said Clark.
"It is so much more complicated than the Enigma machine."