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 $l^+l^-bbar b$ ($l=e,mu$) 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 $ppto Hto ZAto l^+l^-bbar b$. 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 $m_Hge m_A+m_Z$. 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.
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