Can the new resonance at LHC be a CP-Odd Higgs boson?

A plausible explanation of the recent experimental indication of a resonance in the two-photon spectrum at LHC is that it corresponds to the CP-odd Higgs boson. We explore such a possibility in a generic framework of the two Higgs doublet models (2HDM), and combine $m_A \approx 750$GeV with the known $m_h =125.7(4)$~GeV to show that the charged Higgs boson and the other CP-even scalar masses become bounded from bellow and from above. We show that this possibility is also consistent with the electroweak precision data and the low energy observables, which we test in a few leptonic and semileptonic decay modes.