  We consider the minimal supersymmetric standard model within a scenario of
large $\tan\beta$ and heavy squarks and gluinos, with masses of the heavy
neutral Higgs bosons below the TeV scale. We allow for the presence of a large,
model independent, source of lepton flavor violation (LFV) in the slepton mass
matrix in the $\tau-\mu$ sector by the mass insertion approximation. We
constrain the parameter space using the $\tau$ LFV decays together with the
$B$-mesons physics observables, the anomalous magnetic moment of the muon and
the dark matter relic density. We further impose the exclusion limit on
spin-independent neutralino-nucleon scattering from CDMS and the recent CDF
limit from direct search of the heavy neutral Higgs at the TEVATRON. We
re-examine the prospects for the detection of Higgs mediated LFV at LHC, at a
photon collider and in LFV decays of the $\tau$ such as $\tau\to\mu\eta$,
$\tau\to\mu\gamma$. We find rates probably too small to be observed at future
experiments if models have to accommodate for the relic density measured by
WMAP and explain the $(g-2)_{\mu}$ anomaly: better prospects are found if these
two constraints are applied only as upper bounds. The spin-independent
neutralino-nucleon cross section in the studied constrained parameter space is
just below the present CDMS limit and the running XENON100 experiment will
cover the region of the parameter space where the lightest neutralino has large
gaugino-higgsino mixing.
