Surface A(Li) of the Li-rich stars discov- ered so far. Upper left panel: behaviour of A(Li)_NLTE as function of log(L/L_⊙) for all the metal-poor ([Fe/H]<⁻1 dex) Li-rich stars discovered so far. Green circles are Milky Way field stars, blue cir- cles are globular-cluster stars, and the red squares mark HE 0057-5959. The stars of the metal-poor ([Fe/H]~−2.0 dex) globular cluster NGC 6397 (grey circles, Lind et al. 2009) are shown as a reference (and to identify the luminosity of the FDU and RGBb). Upper right panel: run of A(Li)_NLTE as func- tion of [Fe/H] for the Li-rich stars located before the FDU. Red dashed line indicates the WMAP/SBNN A(Li) (Coc & Vangioni 2017). The cyan circles are Li-normal Milky Way field stars (Ryan et al. 1999; Lucatello et al. 2003; Ivans et al. 2005; Asplund et al. 2006; Sivarani et al. 2006; Thompson et al. 2008; Sbordone et al. 2010; Masseron et al. 2012; Ito et al. 2013; Hansen et al. 2014; Bonifacio et al. 2015; Li et al. 2015; Placco et al. 2016; Matsuno et al. 2017; Aguado et al. 2018; Bonifacio et al. 2018). Lower-left panel: run of A(Li)_NLTE as function of [Fe/H] for the Li-rich stars located after the com- pletion of FDU and before the RGBb. The open cir- cle indicates the star 2MASS J19524490-6008132 with an uncertain attribution to this group. The cyan circles are Li-normal Milky Way field stars (Mucciarelli et al. 2022). Lower right panel: run of A(Li)NLTE as function of [Fe/H] for the Li-rich stars located after the RGBb. Open circle indicates the star GSC 03797-00204 with an uncertain attribution to this group.