  We discuss flavor-violating constraints and consequently possible charged
Higgs boson phenomenology emerging from a four-zero Yukawa texture embedded
within the Type-III 2-Higgs Doublet Model (2HDM-III). Firstly, we show in
detail how we can obtain several kinds of 2HDMs when some parameters in the
Yukawa texture are absent. Secondly, we present a comprehensive study of the
main B-physics constraints on such parameters induced by flavor-changing
processes, in particular on the off-diagonal terms of such a texture: i.e.,
from $\mu -e$ universality in $\tau$ decays, several leptonic B-decays ($B \to
\tau \nu$, $D \to \mu \nu$ and $D_s \to {l} \nu$), the semi-leptonic transition
$B\to D \tau \nu$, plus $B \to X_s \gamma$, including $B^0-\bar B^0$ mixing,
$B_s \to \mu^+ \mu^-$ and the radiative decay $Z\to b \bar{b}$. Thirdly, having
selected the surviving 2HDM-III parameter space, we show that the $H^- c
\bar{b}$ coupling can be very large over sizable expanses of it, in fact, a
very different situation with respect to 2HDMs with a flavor discrete symmetry
(i.e., ${\mathcal{Z}}_2$) and very similar to the case of the Aligned-2HDM
(A2HDM) as well as of models with three or more Higgs doublets. Fourthly, we
study in detail the ensuing $H^\pm$ phenomenology at the Large Hadron Collider
(LHC), chiefly the $c\bar b \to H^+$ production mode and the $H^+\to c\bar b$
decay channel while assuming $\tau^+\nu_\tau$ decays in the former and $t\to
bH^+$ production in the latter, showing that significant scope exists in both
cases.
