We consider the recent LHCb result for Bc→J/ψτν in conjunction with the existing anomalies in R(D) and R(D⋆) within the framework of a right-handed current with enhanced couplings to the third generation. The model predicts a linear relation between the observables and their SM values in terms of two combinations of parameters. The strong constraints from b→sγ on W−W′ mixing effectively remove one of the combinations of parameters resulting in an approximate proportionality between all three observables and their SM values. To accommodate the current averages for R(D) and R(D⋆), the W′ mass should be near 1 TeV, and possibly accessible to direct searches at the LHC. In this scenario we find that R(J/ψ) is enhanced by about 20% with respect to its SM value and about 1.5σ below the central value of the LHCb measurement. The predicted dΓ/dq2 distribution for B→D(D⋆)τν is in agreement with the measurement and the model satisfies the constraint from the Bc lifetime.