  We present a new method to simultaneously/self-consistently model the mass
distribution of galaxy clusters that combines constraints from strong lensing
features, X-ray emission and galaxy kinematics measurements. We are able to
successfully decompose clusters into their collisionless and collisional mass
components thanks to the X-ray surface brightness, as well as using the
dynamics of cluster members to obtain more accurate masses with the fundamental
plane of elliptical galaxies. Knowledge from all observables is included
through a consistent Bayesian approach in the likelihood or in physically
motivated priors. We apply this method to the galaxy cluster Abell S1063 and
produce a mass model that we publicly release with this paper. The resulting
mass distribution presents a different ellipticities for the intra-cluster gas
and the other large-scale mass components; and deviation from elliptical
symmetry in the main halo. We assess the ability of our method to recover the
masses of the different elements of the cluster using a mock cluster based on a
simplified version of our Abell S1063 model. Thanks to the wealth of
information provided by the mass model and the X-ray emission, we also found
evidence for an on-going merger event with gas sloshing from a smaller
infalling structure into the main cluster. In agreement with previous findings,
the total mass, gas profile and gas mass fraction are consistent with small
deviations from the hydrostatic equilibrium. This new mass model for Abell
S1063 is publicly available as is the software used to construct it through the
\textsc{Lenstool} package.
