  In this work we present a new search strategy for the discovery of staus at
the LHC in the context of the minimal supersymmetric standard model. The search
profits from the large s-channel $b$-quark annihilation production of the heavy
CP-even and CP-odd Higgs bosons (H/A) which can be attained in regions of
$\tan\beta\gg 1$ that avoid the stringent $H/A \to \tau^+ \tau^-$ searches via
decays into stau pairs. We also focus on regions where the staus branching
ratios are dominated by the decays into a tau lepton and the lightest
neutralino. Thus the experimental signature consists of final states made up of
a tau-lepton pair plus large missing transverse energy. We take advantage of
the large stau-pair production cross sections via heavy Higgs boson decays,
which are between one or two orders of magnitude larger than the usual
electroweak production cross sections for staus. A set of basic cuts allow us
to obtain significances of the signal over the SM backgrounds at the discovery
level (5 standard deviations) in the next LHC run with a center-of-mass energy
of 14 TeV and a total integrated luminosity of only 100 fb$^{-1}$.
