It has been intensively discussed if modifications in the dynamics of the Universe at late times is able or not to solve the $H_0$ tension. On the other hand, it has also been argued that the $H_0$ tension is actually a tension on the supernova absolute magnitude $M_B$. In this work, we robustly constraint $M_B$ using Pantheon Supernovae Ia (SN) sample, Baryon Acoustic Oscillations (BAO), and Big Bang Nucleosynthesis (BBN) data, and assess the $M_B$ tension by comparing three theoretical models, namely the standard $Lambda$CDM, the $w$CDM and a non-gravitational interaction (IDE) between dark energy (DE) and dark matter (DM). We find that the IDE model can solve the $M_B$ tension with a coupling different from zero at 95% CL, confirming the results obtained using a $H_0$ prior.
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