  Multiwavelength deep observations are a key tool to understand the origin of
the diffuse light in clusters of galaxies: the intra-cluster light (ICL). For
this reason, we take advantage of the Hubble Frontier Fields survey to
investigate the properties of the stellar populations of the ICL of its 6
massive intermediate redshift (0.3<z<0.6) clusters. We carry on this analysis
down to a radial distance of ~120 kpc from the brightest cluster galaxy. We
found that the average metallicity of the ICL is [Fe/H] ~-0.5, compatible with
the value of the outskirts of the Milky Way. The mean stellar ages of the ICL
are between 2 to 6 Gyr younger than the most massive galaxies of the clusters.
Those results suggest that the ICL of these massive (> 10^15 Msol) clusters is
formed by the stripping of MW-like objects that have been accreted at z<1, in
agreement with current simulations. We do not find any significant increase in
the fraction of light of the ICL with cosmic time, although the redshift range
explored is narrow to derive any strong conclusion. When exploring the slope of
the stellar mass density profile, we found that the ICL of the HFF clusters
follows the shape of their underlying dark matter haloes, in agreement with the
idea that the ICL is the result of the stripping of galaxies at recent times.
