It is a long debated question whether catalytic activities of enzymes, which lie on the millisecond timescale, are possibly already reflected in variations in atomic thermal fluctuations on the pico- to nanosecond timescale. To shed light on this puzzle, the enzyme human acetylcholinesterase in its wild-type form and complexed with the inhibitor huperzine A were investigated by various neutron scattering techniques and molecular dynamics simulations. Previous results on elastic neutron scattering at various timescales and simulations suggest that dynamical processes are not affected on average by the presence of the ligand within the considered time ranges between 10 ps and 1 ns. In the work presented here, the focus was laid on quasi-elastic (QENS) and inelastic neutron scattering (INS). These techniques give access to different kinds of individual diffusive motions and to the density of states of collective motions at the sub-picoseconds timescale. Hence, they permit going beyond the first approach of looking at mean square displacements. For both samples, the autocorrelation function was well described by a stretched-exponential function indicating a linkage between the timescales of fast and slow functional relaxation dynamics. The findings of the QENS and INS investigation are discussed in relation to the results of our earlier elastic incoherent neutron scattering and molecular dynamics simulations.