Chemical properties of stellar populations are a key observable that can be used to shed light on the assembly history of galaxies across cosmic time. In this study, we investigate the distribution and origin of chemical elements in different stellar components of simulated Milky Way-like galaxies in relation to their mass assembly history, stellar age, and metallicity. Using a sample of 23 simulated galaxies from the Auriga project, we analysed the evolution of heavy elements produced by stellar nucleosynthesis. To study the chemical evolution of the stellar halo, bulge, and warm (thick) and cold (thin) discs of the model galaxies, we applied a decomposition method to characterise the distribution of chemical elements at z = 0 and traced back their origin. Our findings indicate that each stellar component has a distinctive chemical trend despite galaxy-to-galaxy variations. Specifically, stellar haloes are α-enhanced relative to other components, representing the oldest populations, with [Fe/H]--0.6 and a high fraction of ex situ stars of ~50%. They are followed by the warm ([Fe/H]--0.1) and cold ([Fe/H] ~ 0) discs, with in situ fractions of ~90% and ~95%, respectively. Alternatively, bulges are mainly formed in situ but host more diverse stellar populations, with [Fe/H] abundance extending over ∼1 dex around the solar value. We conclude that one of the main drivers shaping the chemical properties of the galactic components in our simulations is the age-metallicity relation. The bulges are the least homogeneous component of the sample, as they present different levels of contribution from young stars in addition to the old stellar component. Conversely, the cold discs appear very similar in all chemical properties, despite important differences in their typical formation times. Finally, we find that a significant fraction of stars in the warm discs were in the cold disc component at birth. We discuss the possible connections of this behaviour with the development of bars and interactions with satellites.