  In the context of a project aimed at characterizing the properties of the
so-called Bulge Fossil Fragments (the fossil remnants of the bulge formation
epoch), here we present the first determination of the metallicity distribution
of Liller 1. For a sample of 64 individual member stars we used ESO- MUSE
spectra to measure the equivalent width of the CaII triplet and then derive the
iron abundance. To test the validity of the adopted calibration in the
metal-rich regime, the procedure was first applied to three reference bulge
globular clusters (NGC 6569, NGC 6440, and NGC 6528). In all the three cases,
we found single-component iron distributions, with abundance values fully in
agreement with those reported in the literature. The application of the same
methodology to Liller 1 yielded, instead, a clear bimodal iron distribution,
with a sub-solar component at $\text{[Fe/H]}= -0.48\,$dex ($\sigma = 0.22$) and
a super-solar component at $\text{[Fe/H]}= +0.26\,$dex ($\sigma = 0.17$). The
latter is found to be significantly more centrally concentrated than the
metal-poor population, as expected in a self-enrichment scenario and in
agreement with what found in another bulge system, Terzan 5. The obtained
metallicity distribution is astonishingly similar to that predicted by the
reconstructed star formation history of Liller 1, which is characterized by
three main bursts and a low, but constant, activity of star formation over the
entire lifetime. These findings provide further support to the possibility
that, similar to Terzan 5, also Liller 1 is a Bulge Fossil Fragment.
