  The formation and evolution of light elements in the Universe act as
important cosmological constraints. It has long been assumed that the oldest
stars of the Galaxy display the primordial Li abundance in their outer layers,
although studies of stellar physics have proven that this abundance must have
decreased with time. The primordial Li abundance deduced from the observations
of the cosmic background is larger than the maximum observed in these stars.
Recent observations have given evidence of a large Li abundance dispersion in
very metal-poor stars. Many of these stars are carbon-rich, the carbon-enhanced
metal-poor (CEMP) stars. We address the general question of the observed
abundances in metal-poor stars and we focus our study on the case of CEMP-s
stars. We study how the accretion of the wind of stellar companions, especially
asymptotic giant branch stars, modifies the element abundances of metal-poor
stars and, in particular Li, taking into account the stellar structure and the
hydrodynamic processes that take place after accretion. We compare the results
with the observations of Li and heavier elements in these old stars on the main
sequence. We use the Montr\'eal/Montpellier stellar evolution code, which
includes atomic diffusion and thermohaline convection, to compute the internal
structure of the proto-CEMP-s stars and their evolution, from [Fe/H]=-2.31 down
to [Fe/H]=-5.45. We study a number of cases that vary according to the masses
of the stars, their ages, metallicities, and the distances to their respective
companions. We show that the observations of Li dispersion that is associated
(or not) with carbon enrichment are well accounted for in terms of accretion on
to the metal-poor stars of the winds of stellar companions, with accreted
masses smaller than those considered in previous studies. The derived
primordial value is in accordance with the cosmological results.
