The Fundamental Plane of cluster spheroidal galaxies at z$\sim1.3$.
  Evidence for mass-dependent evolution
  We present spectroscopic observations obtained at the {\it Large Binocular
Telescope} in the field of the cluster XLSSJ0223-0436 at $z=1.22$. We confirm
12 spheroids cluster members and determine stellar velocity dispersion for 7 of
them. We combine these data with those in the literature for clusters
RXJ0848+4453 at $z=1.27$ (8 galaxies) and XMMJ2235-2557 at $z=1.39$ (7
galaxies) to determine the Fundamental Plane of cluster spheroids. We find that
the FP at $z\sim1.3$ is offset and { rotated ($\sim3\sigma$)} with respect to
the local FP. The offset corresponds to a mean evolution
$\Delta$\rm{log}(M$_{dyn}$/L$_B$)=(-0.5$\pm$0.1)$z$. High-redshift galaxies
follow a steeper mass-dependent M$_{dyn}$/L$_B$-M$_{dyn}$ relation than local
ones. Assuming $\Delta$ log$(M_{dyn}/L_B)$=$\Delta$ log$(M^*/L_B)$, higher-mass
galaxies (log(M$_{dyn}$/M$_\odot$)$\geq$11.5) have a higher-formation redshift
($z_f\geq$6.5) than lower-mass ones ($z_f\leq$2 for
log(M$_{dyn}$/M$_\odot$$\leq$10)), with a median $z_f\simeq2.5$ for the whole
sample. Also, galaxies with higher stellar mass density host stellar
populations formed earlier than those in lower density galaxies. At fixed IMF,
M$_{dyn}$/M$^*$ varies systematically with mass and mass density. It follows
that the evolution of the stellar populations (M$^*/L_B$) accounts for the
observed evolution of M$_{dyn}/L_B$ for M$_{dyn}$$>10^{11}$ M$_\odot$ galaxies,
while accounts for $\sim$85\% of the evolution at M$_{dyn}$$<10^{11}$
M$_\odot$. We find no evidence in favour of structural evolution of individual
galaxies, while we find evidences that spheroids later added to the population
account for the observed discrepancy at masses $<10^{11}$ M$_\odot$. [Abridged]
