We consider the recent LHCb result for $B_cto J/psi tau u$ in conjunction with the existing anomalies in $R(D)$ and $R(D^star)$ 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 $bto s gamma$ on $W-W^prime$ 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 $R(D^star)$, the $W^prime$ mass should be near 1 TeV, and possibly accessible to direct searches at the LHC. In this scenario we find that $R(J/psi)$ is enhanced by about 20% with respect to its SM value and about 1.5$sigma$ below the central value of the LHCb measurement. The predicted $dGamma/dq^2$ distribution for $Bto D(D^star) tau u$ is in agreement with the measurement and the model satisfies the constraint from the $B_c$ lifetime.
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