  Motivated by the notorious anomaly in the lepton flavor universality ratios
$R_{D^{(*)}}$, we study the sensitivity of the Large Hadron Collider (LHC) to a
low-mass charged Higgs boson $H^-$ lighter than $400\,$GeV in a generic two
Higgs doublet model. A combination of current constraints from the $B_c\to\tau
\nu$ decay, $B_{s}$ meson mixing data, tau sleptons and di-jet searches at the
LHC allows to explain the $R_{D^{(*)}}$ anomaly at the $1\,\sigma$ level by a
low-mass charged Higgs. In this context, we estimate the reach of an LHC search
for resonant $H^-$ production, where the final state contains an energetic
$\tau$ lepton decaying hadronically, a neutrino with large transverse momentum,
and an additional $b$-jet ($pp \to b+\tau_h + \nu$). Requiring the additional
$b$-tagged jet in the $\tau\nu$ resonance search profits from the suppression
of the Standard Model background, and therefore it allows us to judge the
low-mass $H^-$ interpretation of the $R_{D^{(*)}}$ anomaly. To demonstrate
this, we perform a fast collider simulation for the $\tau \nu$ resonance search
with an additional $b$-tagged jet, and find that most of the interesting
parameter region of the whole mass range can already be probed with the current
integrated luminosity of $139\,$fb$^{-1}$.
