The hydrogen abstraction reaction between H and H2S, yielding HS and H-2 as products, has been studied within the framework of interstellar surface chemistry. High temperature rate constants below 2000 K are calculated in the gas phase and are in agreement with previously reported values. Subsequently, low-temperature rate constants down to 55 K are presented for the first time that are of interest to astrochemistry, i.e., covering both bimolecular and unimolecular reaction mechanisms. For this, a so-called implicit surface model is used. In strict terms, this is a structural gas phase model in which the restriction of the rotation in the solid state is taken into account. The calculated kinetic isotope effects are explained in terms of the difference in activation and delocalization. All rate constants are calculated at the UCCSD(T)-F12/cc-VTZ-F12 level of theory. Finally, we show that the energetics of the reaction is affected to an only small extent by the presence of H2O or H2S molecular clusters that simulate an ice surface, calculated at the MPWB1K/def2-TZVP level of theory.