We discuss the possibilities to observe the decays of heavy SUSY Higgs bosons
into supersymmetric particles at the LHC. Such an observation would be of
interest either in a discovery search if sparticle modes are the dominant ones,
or in a study of additional decay modes, bringing information on the SUSY
scenario potentially at work. We will focus on the most promising channel where
the heavy neutral Higgses decay into a pair of next-to-lightest neutralinos,
followed by their decay into two leptons and the LSP, thus leading to four
isolated leptons + missing E_T as the main final state signature. A study with
the CMS detector shows that the background (SM + SUSY) can be sufficiently
suppressed and that in the mass region between m_A = 230 and 450 GeV, for low
and intermediate values of tan beta, the signal would be visible provided
neutralinos and sleptons are light enough.Comment: 14 pages, 20 figure
