  We study the gas and stellar mass content of galaxy groups and clusters in
the FABLE suite of cosmological hydrodynamical simulations, including the
evolution of their central brightest cluster galaxies (BCGs), satellite
galaxies and intracluster light (ICL). The total gas and stellar mass of FABLE
clusters are in very good agreement with observations and show negligible
redshift evolution at fixed halo mass for $M_{500} \gtrsim 3 \times 10^{14}
M_{\odot}$ at $z \lesssim 1$, in line with recent findings from
Sunyaev-Zel'dovich (SZ)-selected cluster samples. Importantly, the simulations
predict significant redshift evolution in these quantities in the low mass
($M_{500} \sim 10^{14} M_{\odot}$) regime, which will be testable with upcoming
SZ surveys such as SPT-3G. While the stellar masses of FABLE BCGs are in
reasonable agreement with observations, the total stellar mass in satellite
galaxies is lower than observed and the total mass in ICL is somewhat higher.
This may be caused by enhanced tidal stripping of satellite galaxies due to
their large sizes. BCGs are characterised by moderate stellar mass growth at $z
< 1$ coincident with a late-time development of the ICL. The level of BCG mass
growth is in good agreement with recent observations, however, we caution that
the inferred growth depends sensitively on the mass definition. We further show
that in-situ star formation contributes more than half the mass of a BCG over
its lifetime, the bulk of which is gained at $z > 1$ where star formation rates
are highest. The stellar mass profiles of the BCG+ICL component are similar to
observed profiles out to $\sim 100$ kpc at $z \approx 0$ and follow a close to
power law shape out to several hundred kpc. We further demonstrate that the
inferred size growth of BCGs can be severely biased by the choice of parametric
model and the outer radius of the fit.
