In this paper, we present the Monte-Carlo simulation that we developed and used to design and to interpret the data of a new kind of lifetime spectrometer especially constructed for the determination of the ortho-positronium (o-Ps) re-emission yield from thin mesoporous silica films. The main issue was to have the detection efficiency independent of the o-Ps re-emission energy. This was done in order to avoid a bias of the results related to the positron implantation energy. Furthermore, the simulation is used to calculate the detection efficiencies for annihilation events yielding 2 and 3 gamma photons allowing a precise evaluation of the absolute yield of o-Ps produced in the samples. Calculations were performed using the GEANT4 package. New classes were written to describe the different decay types related to the Ps formation in matter. Moreover, the propagation and interaction of the o-Ps reemitted in a vacuum cavity were also included in the simulation.