Absorbing corrections due to supersymmetric particles to Higgs couplings in effective parameters in the decay H $\to$ hh

Since the Large Hadron Collider (LHC) has not discovered any supersymmetric (SUSY) partners to Standard Model (SM) particles yet, they are likely to exist at higher mass scales. The SUSY particles also contribute indirectly in higher-order corrections to the Higgs boson observables of the extended Higgs sector of the minimal supersymmetric extension of the SM (MSSM), namely to the partial decay widths of Higgs-to-Higgs decays. We compute the higher order corrections to the decay H $\to$ hh of the heavier of the two CP-even Higgs bosons, H, into a pair of lighter SM-like Higgs bosons, h. Assuming the SUSY particles to be very heavy we use an effective 2-Higgs-doublet model. We thoroughly investigate the correct matching conditions to the underlying full theory of the MSSM with heavy superpartners and compare the effective 2HDM-like calculation with the full MSSM result. We delineate the parameter regions where this approximation is valid.