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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 Ca II 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 subsolar component at [Fe/H] = −0.48 dex (σ = 0.22) and a supersolar component at [Fe/H] = +0.26 dex (σ = 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 that 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, Liller 1 is also a Bulge Fossil Fragment. [ABSTRACT FROM AUTHOR]