Unified resolution of the $R(D)$ and $R(D^*)$ anomalies and the lepton flavor violating decay $h\to\mu\tau$

Taking advantage of the fact that the flavor of the neutrino in semileptonic $B$ decays $B\to D^{(*)}\tau\nu$ is not known, we show how a minimal set of higher-dimensional lepton flavor violating (LFV) operators can explain the $R(D^{(*)})$ anomalies, and as a spin-off, can give rise to the LFV decay of the Higgs boson, $h\to\mu\tau$. We also show how none but the minimal set of operators survive the present data.