  The cosmological Li problem is the observed discrepancy between Li abundance,
A(Li), measured in Galactic dwarf, old and metal-poor stars (traditionally
assumed to be equal to the initial value A(Li)_0), and that predicted by
standard Big Bang Nucleosynthesis calculations (A(Li)_{BBN}). Here we attack
the Li problem by considering an alternative diagnostic, namely the surface Li
abundance of red giant branch stars that in a colour magnitude diagram populate
the region between the completion of the first dredge-up and the red giant
branch bump. We obtained high-resolution spectra with the FLAMES facility at
the Very Large Telescope for a sample of red giants in the globular cluster
M54, belonging to the Sagittarius dwarf galaxy. We obtain A(Li)=+0.93+-0.11
dex, translating -- after taking into account the dilution due to the dredge
up-- to initial abundances (A(Li)_0) in the range 2.35--2.29 dex, depending on
whether or not atomic diffusion is considered. This is the first measurement of
Li in the Sagittarius galaxy and the more distant estimate of A(Li)_0 in old
stars obtained so far. The A(Li)_0 estimated in M54 is lower by ~0.35 dex than
A(Li)_{BBN}, hence incompatible at a level of ~3sigma. Our result shows that
this discrepancy is a universal problem concerning both the Milky Way and
extra-galactic systems. Either modifications of BBN calculations, or a
combination of atomic diffusion plus a suitably tuned additional mixing during
the main sequence, need to be invoked to solve the discrepancy.
