Particle therapy positron emission tomography (PT-PET) allows for an in vivo and in situ verification of applied dose distributions in ion beam therapy. Since the dose distribution cannot be extracted directly from the β(+)-activity distribution gained from the PET scan the validation is done by means of a comparison between the reconstructed β(+)-activity distributions from a PT-PET measurement and from a PT-PET simulation. Thus, the simulation software for generating PET data predicted from the treatment planning is an essential part of the dose verification routine. For the dose monitoring of intra-fractionally moving target volumes the PET data simulation needs to be upgraded by using time resolved (4D) algorithms to account correctly for the motion dependent displacement of the positron emitters. Moreover, it has to consider the time dependent relative movement between target volume and scanned beam to simulate the accurate positron emitter distribution generated during irradiation. Such a simulation program is presented which properly proceeds with motion compensated dose delivery by scanned ion beams to intra-fractionally moving targets. By means of a preclinical phantom study it is demonstrated that even the sophisticated motion-mitigated beam delivery technique of range compensated target tracking can be handled correctly by this simulation code. The new program is widely based on the 3D PT-PET simulation program which had been developed at the Helmholtz-Zentrum Dresden-Rossendorf, Germany (HZDR) for application within a pilot project to simulate in-beam PET data for about 440 patients with static tumor entities irradiated at the former treatment facility of the GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany (GSI). A simulation example for a phantom geometry irradiated with a tracked (12)C-ion beam is presented for demonstrating the proper functionality of the program.