The treatment of dynamic solvent effects using variational transition state theory is extended to include quantum effects in an approximate manner. The resulting theory is then applied to the same model system as in Part I for a reaction in solution, namely a collinear model of a triatomic atom-transfer reaction in which the dynamic solvent effects are those of the solvent friction described by a generalized Langevin equation. It is found that dynamic solvent effects on reaction rate constants can be greatly enhanced when quantum mechanical effects are included. Treatment of the reaction model using a classical mechanical theory such as classical variational transition state theory or Grote-Hynes theory typically leads to the solvent friction decreasing the rate constant by factors less than 10. Over the same range of model parameters, the quantum mechanical variational transition-state theory shows decreases as large as several orders of magnitude.