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 µ − e universality in τ decays, several leptonic B-decays (B → τ ν, D → µν and D s → lν), the semi-leptonic transition B → Dτ ν, plus B → X s γ, including B 0 −B 0 mixing, B s → µ + µ − and the radiative decay Z → bb. Thirdly, having selected the surviving 2HDM-III parameter space, we show that the H − cb 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., 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 ± phenomenology at the Large Hadron Collider (LHC), chiefly the cb → H + production mode and the H + → cb decay channel while assuming τ + ν τ decays in the former and t → bH + production in the latter, showing that significant scope exists in both cases.