From Hubble Frontier Fields photometry, and data from the Multi Unit Spectroscopic Explorer on the Very Large Telescope, we build the Fundamental Plane (FP) relation for the early-type galaxies of the cluster Abell S1063. We use this relation to develop an improved strong lensing model of the total mass distribution of the cluster, determining the velocity dispersions of all 222 cluster members included in the model from their measured structural parameters. Fixing the hot gas component from X-ray data, the mass density distributions of the diffuse dark matter haloes are optimised by comparing the observed and model-predicted positions of 55 multiple images of 20 background sources, distributed over the redshift range $0.73-6.11$. We determine the uncertainties on the model parameters with Monte Carlo Markov chains. Compared to previous works, our model allows for the inclusion of a scatter on the relation between the total mass and the velocity dispersion of cluster members, which also shows a shallower slope. We notice a lower statistical uncertainty on the value of some parameters, such as the core radius, of the diffuse mass component of the cluster. Thanks to a new estimate of the stellar mass of all members, we measure the projected, cumulative mass profiles out to a radius of 350 kpc, for all baryonic and dark matter components of the cluster. At the outermost radius, we find a baryon fraction of $0.147 pm 0.002$. We compare the sub-haloes as described by our model with recent hydrodynamical cosmological simulations. We find good agreement in terms of stellar mass fraction. On the other hand, we report some discrepancies in terms of maximum circular velocity, which is an indication of their compactness, and sub-halo mass function in the central cluster regions.
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