  By borrowing the results from a Large Hadron Collider (LHC) analysis
performed with $36.1~\text{fb}^{-1}$ of Run 2 data intended to search for $A$
production followed by $ZH$ decay in turn yielding $l^+l^-b\bar b$ ($l=e,\mu$)
final states in the context of the standard four Yukawa types of the 2-Higgs
Doublet Model (2HDM), we recast it in terms of sensitivity reaches for the
similar process $pp\to H\to ZA\to l^+l^-b\bar b$. This simple exercise across
the two processes, which is possible because the only kinematic difference
between these are different widths for the Higgs bosons, in turn affecting
minimally the efficiency of an experimental selection, enables us to expand the
region of parameter space that can be tested to the case when $m_H\ge m_A+m_Z$.
Furthermore, we extrapolate our results to full Run 3 data samples. We conclude
that, while the high energy and luminosity stage of the LHC can afford one with
increased sensitivity to the 2HDM in general, the recast analysis does not add
anything to what already probed through the actual one.
