  Still largely unexplored, the diffuse light in cluster of galaxies traces the
past and on-going buildup of these massive structures. Here, we present the
first comprehensive study of the intracluster light (ICL) of the cluster
SMACS-J0723.3-7327 (z=0.39) using the JWST Early Release Observations. These
deep and high spatial resolution images allow the study of the ICL with high
signal-to-noise ratio up to a radial distance of $\sim400$ kpc, twice as far
with respect to previous HST studies of intermediate redshift clusters. This
opens up the possibility of exploring the rich mixture of processes that are
building the ICL. We find that the inner parts (R$<$100 kpc) are built through
a major merger while the outer parts (R$>$ 100 kpc) are mainly produced by the
tidal stripping of Milky Way-like satellites. We also found that the slope of
the stellar mass density radial profile of the ICL of this cluster
($\alpha_{3D} = -2.47\pm0.13$) follows closely the predicted dark matter halo
slope ($\alpha_{3D\mathrm{,DM}} = -2.6$ to $-2$), supporting the idea that both
components have a similar shape and thus the potential of using the ICL as a
tracer of the dark matter distribution in clusters of galaxies. Future JWST
studies of the ICL are set to revolutionise our understanding of cluster
formation and will be crucial to improve the gravitational lensing mass maps of
these structures and thus to accurately characterise the properties of the
first galaxies.
