At the FRS Ion Catcher at GSI, projectile and fission fragments are produced at relativistic energies, separated in-flight, range-focused, slowed down and thermalized in a cryogenic stopping cell. A multiple-reflection time-of-flight mass spectrometer (MR-TOF-MS) is used to perform direct mass measurements and to provide an isobarically clean beam for further experiments, such as mass-selected decay spectroscopy. A versatile RF quadrupole transport and diagnostics unit guides the ions from the stopping cell to the MR-TOF-MS, provides differential pumping, ion identification and includes reference ion sources. The FRS Ion Catcher serves as a test facility for the Low-Energy Branch of the Super-FRS at the Facility for Antiproton and Ion Research (FAIR), where the cryogenic stopping cell and the MR-TOF-MS will be key devices for the research with stopped projectile and fission fragments that will be performed with the experiments MATS and LaSpec. Off-line tests of the stopping cell yield a combined ion survival and extraction efficiency for 219Rn ions of about 30% and an extraction time of about 25 ms. The stopping cell and the MR-TOF-MS were commissioned on-line as part of the FRS Ion Catcher. For the first time, a stopping cell for exotic nuclei was operated on-line at cryogenic temperatures. Using a gas density almost two times higher than ever reached before for a stopping cell with RF ion repelling structures, various 238U projectile fragments were thermalized and extracted with very high efficiency. Direct mass measurements of projectile fragments were performed with the MR-TOF-MS, among them the nuclide 213Rn with a half-life of 19.5 ms only.