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The Alpha Magnetic Spectrometer (AMS) is a particle physics experiment based on the International Space Station (ISS). At the heart of the detector is a large superconducting magnet, cooled to a temperature of 1.8 K by superfluid helium. The magnet and cryogenic system have been designed and built by Scientific Magnetics (formerly Space Cryomagnetics) of Culham, England. This paper describes the results from magnet testing, and the final assembly of the magnet and flight cryostat.