Primordial black holes (PBHs) are one of the most promising astrophysical objects in the study of beyond Standard Model physics. In addition, axion-like particles (ALPs) are one of the well-motivated particles beyond the Standard Model. Therefore, understanding the properties of PBHs and ALPs is important. In this work, we study their properties through the ALPs emitted by the Hawking radiation of extra-galactic PBHs. We compare the direct photon spectrum from PBHs and the additional contribution via the ALPs produced from PBHs with the expected sensitivity of e-ASTROGAM. Finally, we obtain improved future limits on the axion-photon coupling as well as the fraction of dark matter that PBHs represent today.