Aims. Our goal is to complete the inventory of S-bearing molecules and their abundances in the prototypical photodissociation region (PDR) the Horsehead nebula to gain insight into sulphur chemistry in UV irradiated regions. Based on the WHISPER millimeter (mm) line survey, our goal is to provide an improved and more accurate description of sulphur species and their abundances towards the core and PDR positions in the Horsehead. Methods. The Monte Carlo Markov chain (MCMC) methodology and the molecular excitation and radiative transfer code RADEX were used to explore the parameter space and determine physical conditions and beam-averaged molecular abundances. Results. A total of 13 S-bearing species (CS, SO, SO2, OCS, H2CS - both ortho and para - HDCS, C2S, HCS+, SO+, H2S, S2H, NS and NS+) have been detected in the two targeted positions. This is the first detection of SO+ in the Horsehead and the first detection of NS+ in any PDR. We find a differentiated chemical behaviour between C-S and O-S bearing species within the nebula. The C-S bearing species C2S and o-H2CS present fractional abundances a factor grater than two higher in the core than in the PDR. In contrast, the O-S bearing molecules SO, SO2, and OCS present similar abundances towards both positions. A few molecules, SO+, NS, and NS+, are more abundant towards the PDR than towards the core, and could be considered as PDR tracers. Conclusions. This is the first complete study of S-bearing species towards a PDR. Our study shows that CS, SO, and H2S are the most abundant S-bearing molecules in the PDR with abundances of a few 1E-9. We recall that SH, SH+, S, and S+ are not observable at the wavelengths covered by the WHISPER survey. At the spatial scale of our observations, the total abundance of S atoms locked in the detected species is < 1E-8, only ~0.1% of the cosmic sulphur abundance.