  We investigate the characteristics of the gamma-ray signal following the
decay of MeV-scale Axion-Like Particles (ALPs) coupled to photons which are
produced in a Supernova (SN) explosion. This analysis is the first to include
the production of heavier ALPs through the photon coalescence process,
enlarging the mass range of ALPs that could be observed in this way and giving
a stronger bound from the observation of SN 1987A. Furthermore, we present a
new analytical method for calculating the predicted gamma-ray signal from ALP
decays. With this method we can rigorously prove the validity of an
approximation that has been used in some of the previous literature, which we
show here to be valid only if all gamma rays arrive under extremely small
observation angles (i.e. very close to the line of sight to the SN). However,
it also shows where the approximation is not valid, and offers an efficient
alternative to calculate the ALP-induced gamma-ray flux in a general setting
when the observation angles are not guaranteed to be small. We also estimate
the sensitivity of the Fermi Large Area Telescope (Fermi-LAT) to this gamma-ray
signal from a future nearby SN and show that in the case of a non-observation
the current bounds on the ALP-photon coupling $ g_{a\gamma} $ are strengthened
by about an order of magnitude. In the case of an observation, we show that it
may be possible to reconstruct the product $ g_{a\gamma}^2 m_a $, with $ m_a $
the mass of the ALP.
