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Context. The 1.8 MeVγ-rays corresponding to the decay of the radioactive isotope²⁶Al (with a half-life of 0.72 Myr ) have been observed by the SPI detector on the INTEGRAL spacecraft and extensively used as a tracer of star formation and current nucleosynthetic activity in the Milky Way Galaxy. Further information is encoded in the observation related to the higher²⁶Al content found in regions of the Galaxy with the highest line-of-sight (LoS) velocity relative to an observer located in the Solar System. However, this feature remains unexplained. Aims. We ran a cosmological “zoom-in” chemodynamical simulation of a Milky Way-type galaxy, including the production and decays of radioactive nuclei in a fully self-consistent way. We then analyzed the results to follow the evolution of²⁶Al throughout the lifetime of the simulated galaxy to provide a new method for interpreting the²⁶Al observations. Methods. We included the massive star sources of²⁶Al in the Galaxy and its radioactive decay into a state-of-the-art galactic chemical evolution model, coupled with cosmological growth and hydrodynamics. This approach allowed us to follow the spatial and temporal evolution of the²⁶Al content in the simulated galaxy. Results. Our results are in agreement with the observations with respect to the fact that gas particles in the simulation with relatively higher²⁶Al content also have the highest LoS velocities. On the other hand, gas particles with relatively lower²⁶Al content (i.e., not bright enough to be observed) generally display the lowest LoS velocities. However, this result is not conclusive because the overall rotational velocity of our simulated galaxy is higher than that observed for cold CO gas in the Milky Way Galaxy. Furthermore, we found no significant correlation between gas temperature, rotational velocity, and²⁶Al content at any given radius. We also found the presence of transient²⁶Al-rich spots at low LoS velocities and we show that one such spot had been captured by the INTEGRAL/SPI data. Based on our model, we present a prediction for the detection of 1.8 MeVγ-rays by the future COSI mission. We find that according to our model, the new instrument will be able to observe similar²⁶Al-emission patterns to those seen by INTEGRAL/SPI.