The integration of MSRs into marine reactor applications is advancing, primarily due to their potential to offer safer and mobile energy solutions. While safety studies are crucial for such marine reactor applications, it is equally important to investigate the changes in the inventory of nuclear material isotopes from a non-proliferation perspective. Therefore, this study aims to analyze the non-proliferation aspects by tracking isotopic variations during reactor operation. For that, the Molten Salt Reactor Experiment (MSRE), a research reactor at Oak Ridge National Laboratory (ORNL), was simulated using Serpent 2 to replicate its four-year operational period. The simulation accounted for real-time operational conditions, including the removal of fission products, primarily noble gases such as xenon and krypton, and refueling of uranium-233. The depletion simulation was divided into three phases: first, the MSRE began with fresh fuel of uranium-235, with fission product removal implemented to maintain reactivity; second, uranium-233, bred from thorium-232, was introduced as a new fuel source, demonstrating the reactor's shift to a thorium-based fuel cycle; finally, the reactor operated with a combination of uranium-235 and uranium-233 , with periodic noble gas removal to sustain system stability. By applying the conducted simulation, this design aims to operate the MSRE for a 25-year ship service life through repeated cycles of phases 2 and 3. Feasibility of MSRE in the marine application is analyzed based on that simulations. Moreover, the Pu quality and quantity is analyzed as a function of burnup for the purpose of the non-proliferation study.