  Experimental measurements collected by the BABAR, Belle, and LHCb experiments
on different observables associated with the semileptonic transition $b \to c
\tau \bar{\nu}_\tau$, indicate the existence of disagreement respect with the
Standard Model predictions. We analyse the charged scalar boson contributions
to these charged-current $B$ meson anomalies within the framework of two Higgs
doublet model with the most general Yukawa couplings to quarks and leptons from
the third generation, involving left-handed and right-handed (sterile)
neutrinos. We perform a phenomenological study of the Yukawa couplings
parameter space that accommodates these anomalies. We consider the most recent
data from HFLAV world-average and Belle combination, and the upper limits ${\rm
BR}(B_c^- \to \tau^- \bar{\nu}_{\tau}) < 30\%$ and $10\%$. In addition, we
include in our study the prospect measurements on $R(D^{(\ast)})$ that the
Belle II experiment could achieve and explore, for the first time, the future
implications for the corresponding charged scalar Yukawa couplings. This
analysis updates the existing literature and includes new important
observables. Our results show that current experimental $b\rightarrow c \tau
\bar{\nu}_\tau$ data and Belle II projection favor the interpretation of a
charged scalar boson interacting with right-handed neutrinos. Furthermore, as a
side analysis regarding the charged scalar boson interpretation, we revisit the
relation between $R(D^\ast)$ and ${\rm BR}(B_c^- \to \tau^- \bar{\nu}_{\tau})$
by investigating whether the claim that pseudoscalar new physics
interpretations of $R(D^{\ast})$ are implausible due to the $B_c$ lifetime is
still valid, to the light of the recent data and Belle II prospects on
$R(D^{\ast})$. Lastly, we reexamine addressing the $R(D^{(\ast)})$ anomalies in
the context of the 2HDM of Type II.
