  We study the process q q, g g -> A -> Z* h in a 2-Higgs Doublet Model Type-II
where the mass of the CP-odd Higgs state A is lower than the rest mass of the Z
and h particles (the latter being the Standard Model-like Higgs state), i.e.,
mA < mZ + mh = 215 GeV. This is a mass range which is not being currently
tested by ATLAS and CMS in this channel, yet we show that there can be
sensitivity to it already during Runs 2 and 3, assuming leptonic decays of the
gauge boson and bottom-antibottom quark ones for the Higgs boson.
