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The ATLAS and CMS Collaborations have observed independently at the LHC a new Higgs-like particle with a mass and properties similar to that predicted by the Standard Model (SM). Although the measurements indicate that this Higgs-like boson is compatible with the SM hypothesis, due to large uncertainties in some of the Higgs detection channels, one still has the possibility of testing this object as being a candidate for some beyond the SM physics scenarios, for example, the minimal supersymmetric Standard Model (MSSM), in the -conserving version (CPC-MSSM). In this paper, we evaluate the modifications of these CPC-MSSM results when -violating (CPV) phases are turned on explicitly, leading to the -violating MSSM (CPV-MSSM). We investigate the effect of the CPV phases in (some of) the soft supersymmetry (SUSY) terms on both the mass of the lightest Higgs boson , and the rates for the processes  …