  We study the phenomenology of charged Higgs bosons ($H^\pm$) and Vector-Like
Quarks (VLQs), denoted as $T$, the latter possessing a charge identical to the
top quark one, within the framework of the Two Higgs Doublet Model Type-II
(2HDM-II). Upon examining two scenarios, one featuring a singlet $(T)$
(2HDM-II+$(T)$) and another a doublet $(TB)$ (2HDM-II+$(TB)$), we discover that
the presence of VLQs has a significant effect on the (pseudo)scalar sector of
the 2HDM-II. In particular, this leads to a reduction in the strict constraint
on the mass of the charged Higgs boson, which is imposed by $B$-physics
observables, specifically $B\to X_s\gamma$. {The observed reduction stems from
modifications in the charged Higgs couplings to the Standard Model (SM) top and
bottom quarks}. Notably, the degree of this reduction varies distinctly between
the singlet 2HDM+$(T)$ and doublet 2HDM+$(TB)$ scenarios. Additionally, our
investigation extends to constraints imposed by the oblique parameters $S$ and
$T$ on the VLQ mixing angles. Furthermore, to facilitate efficient exploration
of the '2HDM-II+VLQ' parameter space, we present results on pair production of
VLQs $T$ ($pp\to T\bar T$), followed by $T\to H^\pm b$ and $H^\pm \to tb$
decays, yielding a distinctive $2t4b$ final state. This investigation thus
provides valuable insights guiding the search for extended Higgs and quark
sectors at the Large Hadron Collider (LHC) at CERN.
