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The high cosmic abundance and the intermediate volatility and chemical properties of sulfur allow the use of sulfur-bearing species as a tracer of the chemical processes in the atmospheres of hot Jupiter exoplanets. Nevertheless, despite its properties and relevance as a tracer of the giant planets' formation history, little attention has been paid to this species in the context of hot Jupiter atmospheres. Here we provide an overview of the abundances of sulfur-bearing species in hot Jupiter atmospheres under different conditions and explore their observability. We use the photochemical kinetics code VULCAN to model hot Jupiter atmospheric disequilibrium chemistry. Transmission spectra for these atmospheres are created using the modelling framework ARCiS. We vary model parameters such as the diffusion coefficient, and we study the importance of photochemistry on the resulting mixing ratios. Furthermore, we vary the chemical composition of the atmosphere by increasing the metallicity from solar to ~10 times solar. We also explore different C/O ratios. We find that H2S and SO2 are the best candidates for detection between 1 and 10 micron, using a spectral resolution that is representative of the instruments on board the JWST. H2S is easiest to detect at an equilibrium temperature of ~1500 K and C/O ratios between 0.7 and 0.9, with the ideal value increasing slightly for increasing metallicity. SO2 is most likely to be detected at an equilibrium temperature of ~1000 K at low C/O ratios and high metallicities. Nevertheless, among these two molecules, we expect SO2 detection to be more common, as it is detectable in scenarios more favoured by formation models. We conclude that H2S and SO2 will most likely be detected in the coming years with the JWST and that the detection of these species will provide information on atmospheric processes and planet formation scenarios.