  Strong gravitational lensing (SL) has emerged as a very accurate probe of the
mass distribution of cluster- and galaxy-scale dark matter (DM) haloes in the
inner regions of galaxy clusters. The derived properties of DM haloes can be
compared to the predictions of high-resolution cosmological simulations,
providing us with a test of the Standard Cosmological Model. The usual choice
of simple power-law scaling relations to link the total mass of members with
their luminosity is one of the possible inherent systematics within SL models
of galaxy clusters, and thus on the derived cluster masses. Using new
information on their structural parameters (from HST imaging) and kinematics
(from MUSE data), we build the Fundamental Plane (FP) for the early-type
galaxies of the cluster Abell S1063. We take advantage of the calibrated FP to
develop an improved SL model of the total mass of the cluster core. The new
method allows us to obtain more accurate and complex relations between the
observables describing cluster members, and to completely fix their mass from
their observed magnitudes and effective radii. Compared to the power-law
approach, we find a different relation between the mass and the velocity
dispersion of members, which shows a significant scatter. Thanks to a new
estimate of the stellar mass of the cluster members from HST data, we measure
the cumulative projected mass profiles out to a radius of 350 kpc, for all
baryonic and DM components of the cluster. Finally, we compare the physical
properties of the sub-haloes in our model and those predicted by
high-resolution hydrodynamical simulations. We obtain compatible results in
terms of the stellar-over-total mass fraction of the members. On the other
hand, we confirm the recently reported discrepancy in terms of sub-halo
compactness: at a fixed total mass value, simulated sub-haloes are less compact
than what our SL model predicts.
