Abstract
In the Minimal Supersymmetric Standard Model (MSSM) the mass of the lightest neutral Higgs boson is determined by the supersymmetric parameters. In the $m_h$MSSM the precisely measured Higgs boson replaces the trilinear coupling $A_t$ as input parameter. Expressions are derived to extract $A_t$ in a semi-analytical form as a function of the light Higgs boson (pole) mass. An algorithm is developed and implemented at two--loop precision, generalizable to higher orders, to perform this inversion consistently. The result of the algorithm, implemented in the SuSpect spectrum calculator, is illustrated on a parameter set compatible with LHC measurements.