Photolysis of H2S adsorbed on LiF(001) was studied by means of hydrogen Rydberg-atom time-of-flight spectroscopy. The H-atom translational energy distributions using 193.3 nm radiation showed three main features: a high energy channel attributed to H atoms escaping the surface without collisions (DIR); a vibrational progression from v=0 to v=5 [EL(v=0) and INEL(v > 0)]; and a low energy channel attributed to multiple inelastic collisions [INEL(2)]. The vibrational progression can be attributed to two concurrent processes: the primary production of vibrationally excited SH in the dissociative event, and a secondary T-->V energy transfer between the outgoing translationally hot H atom and a neighboring H2S(ad) molecule. The coverage dependence and angular distribution of the DIR, EL, and the INEL(v > 0) channels has been used to define a minimum set of required H2S(ad) geometries.