Position in Hertzsprung-Russell diagram of the target star HE 0057-5959 (red square) and of the other metal-poor ([Fe/H]<−1 dex) Li-rich stars discovered so far (see details in Sect. 4): green circles are Galactic-field stars and blue circles are globular-cluster stars. Two theoretical isochrones with [Fe/H]=−3.2 and −1.2 dex, an α-enhanced chemical mixture, and an age of 13 Gyr (Pietrinferni et al. 2021) are shown for reference (black curves). The two grey shaded areas indicate the loci where the drops of A(Li)_nlte due to the FDU and further extra-mixing episodes, respectively, occur.