The recent discovery of a SM-like Higgs boson at the LHC, with a mass around 125-126 GeV, together with the absence of results in the direct searches for supersymmetry, is pushing the SUSY scale (mSUSY) into the multi-TeV range. This discouraging situation from a low-energy SUSY point of view has its counterpart in indirect SUSY observables which present a non-decoupling behavior with mSUSY. This is the case of the one-loop lepton avor violating Higgs decay rates induced by SUSY, which are shown here to remain constant as mSUSY grows, for large mSUSY > 2TeV values and for all classes of intergenerational mixing in the slepton sector, LL, LR, RL and RR. In this work we focus on the LFV decays of the three neutral MSSM Higgs bosons h, H, A → τμ, considering the four types of slepton mixing (σLL 23 , σLR 23 , σRL 23 , σRR 23 ), and show that all the three channels could be measurable at the LHC, being h → τμ the most promising one, with up to about hundred of events expected with the current LHC center-of-mass energy and luminosity. The most promising predictions for the future LHC stage are also included.Instituto de Física La Plata