The accuracy of Monte Carlo simulations in reproducing the scientific performance of space telescopes (e.g. angular resolution) is mandatory for a correct design of the mission. A brand-new Monte Carlo simulator of the Astrorivelatore Gamma ad Immagini LEggero (AGILE)/Gamma-Ray Imaging Detector (GRID) space telescope, AGILESim, is built using the customizable Bologna Geant4 Multi-Mission Simulator (BoGEMMS) architecture and the latest Geant4 library to reproduce the instrument performance of the AGILE/GRID instrument. The Monte Carlo simulation output is digitized in the BoGEMMS postprocessing pipeline, according to the instrument electronic read-out logic, then converted into the onboard data handling format, and finally analyzed by the standard mission on-ground reconstruction pipeline, including the Kalman filter, as a real observation in space. In this paper we focus on the scientific validation of AGILESim, performed by reproducing (i) the conversion efficiency of the tracker planes, (ii) the tracker charge readout distribution measured by the on-ground assembly, integration, and verification activity, and (iii) the point-spread function of in-flight observations of the Vela pulsar in the 100 MeV - 1 GeV energy range. We measure an in-flight angular resolution (FWHM) for Vela-like point sources of $2.0^{+0.2}_{-0.3}$ and $0.8^{+0.1}_{-0.1}$ degrees in the 100 - 300 and 300 - 1000 MeV energy bands, respectively. The successful cross-comparison of the simulation results with the AGILE on-ground and in-space performance validates the BoGEMMS framework for its application to future gamma-ray trackers (e.g. e-ASTROGAM and AMEGO).
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