We use interplanetary transport simulations to compute a database of electron Green's functions, i.e., differential intensities resulting at the spacecraft position from an impulsive injection of energetic (>20 keV) electrons close to the Sun, for a large number of values of two standard interplanetary transport parameters: the scattering mean free path and the solar wind speed. The nominal energy channels of the ACE, STEREO, and Wind spacecraft have been used in the interplanetary transport simulations to conceive a unique tool for the study of near-relativistic electron events observed at 1 AU. In this paper, we quantify the characteristic times of the Green's functions (onset and peak time, rise and decay phase duration) as a function of the interplanetary transport conditions. We use the database to calculate the FWHM of the pitch-angle distributions at different times of the event and under different scattering conditions. This allows us to provide a first quantitative result that can be compared with observations, and to assess the validity of the frequently used term beam-like pitch-angle distribution.