Context. Sulphur is one of the most abundant elements in the Universe (S/H ~ 1.3 × 10⁻⁵) and plays a crucial role in biological systems on Earth. The understanding of its chemistry is therefore of major importance. 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 (Wide-band High-resolution Iram-30 m Surveys at two positions with Emir Receivers) 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 of > 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 approximately a few 10⁻⁹. 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 <10⁻⁸, only ~0.1% of the cosmic sulphur abundance.