  Carbon-enhanced metal-poor stars with s-process enrichment (CEMP-s) are
believed to be the products of mass transfer from an AGB companion, which has
long since become a white dwarf. The surface abundances of CEMP-s stars are
thus commonly assumed to reflect the nucleosynthesis output of the first AGB
stars. We have previously shown that, for this to be the case, some physical
mechanism must counter atomic diffusion in these nearly fully radiative stars,
which otherwise leads to surface abundance anomalies clearly inconsistent with
observations. Here we take into account angular momentum accretion by these
stars. We compute in detail the evolution of typical CEMP-s stars from the
ZAMS, through the mass accretion, and up the RGB for a wide range of specific
angular momentum of the accreted material, corresponding to rotation velocities
between about 0.3 and 300 km/s. We find that only for specific angular momentum
above 1e+17 cm2/s (rotation velocities above 20 km/s) angular momentum
accretion directly causes chemical dilution of the accreted material. This
could nevertheless be relevant to CEMP-s stars, which are observed to rotate
more slowly, if they undergo continuous angular momentum loss akin to
solar-like stars. In models with rotation velocities characteristic of CEMP-s
stars, rotational mixing primarily serves to inhibit atomic diffusion, such
that the maximal surface abundance variations (with respect to the composition
of the accreted material) prior to first dredge-up remain within about 0.4 dex
without thermohaline mixing or about 0.5-1.5 dex with thermohaline mixing. Even
in models with the lowest rotation velocities (under a km/s), rotational mixing
is able to severely inhibit atomic diffusion, compared to non-rotating models.
We thus conclude that it offers a natural solution to the problem posed by
atomic diffusion and cannot be neglected in models of CEMP-s stars.
