  The $A\to Z^{(*)}h$ decay signature has been highlighted as possibly being
the first testable probe of the Standard Model (SM) Higgs boson discovered in
2012 ($h$) interacting with Higgs companion states, such as those existing in a
2-Higgs Doublet Model (2HDM), chiefly, a CP-odd one ($A$). The production
mechanism of the latter at the Large Hadron Collider (LHC) takes place via
$b\bar b$-annihilation and/or $gg$-fusion, depending on the 2HDM parameters, in
turn dictated by the Yukawa structure of this Beyond the SM (BSM) scenario.
Among the possible incarnations of the 2HDM, we test here the so-called
Type-II, for a twofold reason. On the one hand, it intriguingly offers two very
distinct parameter regions compliant with the SM-like Higgs measurements, i.e.,
where the so-called `SM limit' of the 2HDM can be achieved. On the other hand,
in both configurations, the $AZh$ coupling is generally small, hence the signal
is strongly polluted by backgrounds, so that the exploitation of Machine
Learning (ML) techniques becomes extremely useful. In this paper, we show that
the application of advanced ML implementations can be decisive in establishing
such a signal.
  This is true for all distinctive kinematical configurations involving the
$A\to Z^{(*)}h$ decay, i.e., below threshold ($m_A<m_Z+m_h$), at its maximum
($m_Z+m_h<m_A<2m_t$) and near the onset of $t\bar t$ pair production ($m_A
\approx 2m_t$), for which we propose Benchmark Points (BPs) for future
phenomenological analyses.
