A map of surface molecular water was derived from long slit spectroscopy of the south polar region of the Moon using the Faint Object infraRed CAmera for the SOFIA Telescope (FORCAST) spectrometer on the Stratospheric Observatory for Infrared Astronomy (SOFIA). Mean water abundances detected are about 250 µg/g over that of a mare reference surface at Mare Fecunditatis. Water abundances are locally anticorrelated with temperature and latitude. The distribution of water is consistent with derivation of water from pre-existing hydroxyl subsequently trapped in impact glass, provided hydroxyl increases with latitude as some models and measurements suggest. The detected water cannot be in equilibrium with the exosphere because insufficient water is present to maintain the surface abundance. The data are also consistent with a high latitude water-bearing mineral host that may be a precursor to recently detected high latitude hematite.