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Binding energies (BEs) are one of the most important parameters for astrochemical modeling determining, because they govern whether a species stays in the gas-phase or is frozen on the grain surfaces. It is currently known that, in the denser and colder regions of the interstellar medium, sulphur is severely depleted in the gas phase. It has been suggested that it may be locked into the grain icy mantles. However, which are the main sulphur carriers is still a matter of debate. This work aims at establishing accurate BEs of 17 sulphur-containing species on two validated water ice structural models, the proton-ordered crystalline (010) surface and an amorphous water ice surface. We adopted Density Functional Theory (DFT)-based methods (the hybrid B3LYP-D3(BJ) and the hybrid meta-GGA M06-2X functionals) to predict structures and energetics of the adsorption complexes. London's dispersion interactions are shown to be crucial for an accurate estimate of the BEs due to the presence of the high polarizable sulphur element. While on the crystalline model the adsorption is restricted to a very limited number of binding sites with single valued BEs, on the amorphous model several adsorption structures are predicted, giving a BE distribution for each species. With the exception of few cases, both experimental and other computational data are in agreement with our calculated BE values. A final discussion on how useful the computed BEs are with respect to the snow lines of the same species in protoplanetary disks is provided