  The description of the heavy meson production at large energies and forward
rapidities at the LHC is fundamental to derive realistic predictions of the
prompt atmospheric neutrino flux at the IceCube Observatory. In particular, the
prompt tau neutrino flux is determined by the decay of $D_s$ mesons produced in
cosmic ray - air interactions at high energies and large values of the Feynman
- $x_F$ variable. Recent data from the LHCb Collaboration indicate a production
asymmetry for $D_s^+$ and $D_s^-$ mesons, which cannot be explained in terms of
the standard modelling of the hadronization process. In this paper we
demonstrate that this asymmetry can be described assuming an asymmetric strange
sea ($s(x) \ne \bar s(x)$) in the proton wave function and taking into account
of the charm and strange fragmentation into $D_s$ mesons. Moreover, we show
that the strange quark fragmentation contribution is dominant at large - $x_F$
($\ge 0.3$). The prompt $\nu_{\tau}$ flux is calculated and the enhancement
associated to the strange quark fragmentation contribution, disregarded in
previous calculations, is estimated.
