  We present the analysis, based on spectra collected at the Large Binocular
Telescope, of the stellar populations in seven spheroidal galaxies in the
cluster XLSSJ0223 at $z$$\sim$1.22. The aim is to constrain the epoch of their
formation and their star formation history. Using absorption line strenghts and
full spectral fitting, we derive for the stellar populations of the seven
spheroids a median age <Age>=2.4$\pm$0.6 Gyr, corresponding to a median
formation redshift $<$$z_f$$>$$\sim2.6_{-0.5}^{+0.7}$ (lookback time =
11$_{-1.0}^{+0.6}$ Gyr). We find a significant scatter in age, showing that
massive spheroids, at least in our targeted cluster, are not coeval. The median
metallicity is [Z/H]=0.09$\pm$0.16, as for early-types in clusters at
0$<$$z$<0.9. This lack of evolution of [Z/H] over the range 0$<$$z$$<$1.3,
corresponding to the last 9 billions years, suggests that no significant
additional star formation and chemical enrichment are required for cluster
spheroids to reach the present-day population. We do not detect significant
correlation between age and velocity dispersion $\sigma_e$, or dynamical mass
M$_{dyn}$, or effective stellar mass density $\Sigma_e$. On the contrary, the
metallicity [Z/H] of the seven spheroids is correlated to their dynamical mass
M$_{dyn}$, according to a relation similar to the one for local spheroids.
[Z/H] is also anticorrelated to stellar mass density $\Sigma_e$ because of the
anticorrelation between M$_{dyn}$ and $\Sigma_e$. Therefore, the basic trends
observed in the local universe were already established at $z\sim1.3$, i.e.
more massive spheroids are more metal rich, have lower stellar mass density and
tend to be older than lower-mass galaxies.
