The Soft X-ray Spectrometer (SXS) is a cryogenic high-resolution X-ray spectrometer onboard the ASTRO-H satellite, that achieves energy resolution better than 7 eV at 6 keV, by operating the detector array at 50 mK using an adiabatic demagnetization refrigerator. The cooling chain from room temperature to the ADR heat sink is composed of 2-stage Stirling cryocoolers, a He-4 Joule-Thomson cryocooler, and superfluid liquid He, and is installed in a dewar. It is designed to achieve a helium lifetime of more than 3 years with a minimum of 30 liters. The satellite was launched on 2016 February 17, and the SXS worked perfectly in orbit, until March 26 when the satellite lost its function. It was demonstrated that the heat load on the He tank was about 0.7 mW, which would have satisfied the lifetime requirement. This paper describes the design, results of ground performance tests, prelaunch operations, and initial operation and performance in orbit of the flight dewar and cryocoolers.