  The most massive protoclusters virialize to become clusters at $z\sim 2$,
which is also a critical epoch for the evolution of their member galaxies.
XLSSC 122 is a $z=1.98$ galaxy cluster with 37 spectroscopically confirmed
members. We aim to characterize their star formation histories and to put them
in the context of the cluster accretion history. We measure their photometry in
12 bands and create a PSF-matched catalogue of the cluster members. We employ
BAGPIPES to fit star formation histories characterized by exponentially
decreasing star-forming rates. Stellar masses, metal and dust contents are also
treated as free parameters. The oldest stars in the red-sequence galaxies
display a range of ages, from 0.5 Gyr to over $\sim$3 Gyrs. Characteristic
times are between $\sim$0.1 and $\sim$0.3 Gyr, and the oldest members present
the longest times. Using MultiDark Planck 2 dark matter simulations, we
calculate the assembly of XLSSC 122-like haloes, weighted by the age posteriors
of the oldest members. We found that 74% of these haloes were less than 10%
assembled at the onset of star formation, declining to 67% of haloes when such
galaxies had formed 50% of their z=1.98 stellar masses. When 90% of their
stellar masses were formed, 75% of the haloes were less than 30% assembled. The
star formation histories of the red-sequence galaxies seem consistent with
episodes of star formation with short characteristic times. Onset and cessation
of star formation in the oldest galaxies are both likely to precede XLSSC 122
virialization.
