A three-dimensional time-dependent quantum mechanical wavepacket method is used to calculate the state-to-state reaction probabilities at zero total angular momentum for the Li + HF --> LiF + H reaction. Reaction probabilities starting from several different initial HF vibrational-rotational states (v=0,j=0,1,2) and going to all possible open channels are computed over a wide range of energies. A single computation of the wavepacket dynamics yields reaction probabilities from a specific initial quantum state of the reactants to all possible final states over a wide range of energies. The energy dependence of the reaction probabilities shows a broad background structure on which resonances of varying widths are superimposed. Sharp resonance features seem to dominate particularly at low product translational energies. There are marked changes in the energy dependence of the reaction probabilities for different initial or final diatom rotational quantum numbers, but it is noticeable that, for both reactants and products, odd and even rotational quantum numbers give rise to similar features. Our results clearly identify some resonance features which are present in the reaction probability plots for all product and initial states, though they appear in the form of sharp peaks in some plots and sharp dips in others. We speculate that these features arise from reactive scattering resonances which serve to redistribute the flux preferentially to particular product quantum states. The present calculations extend to higher energies than previously published time-independent reactive scattering calculations for this system.