We study the M-type asymptotic giant branch (AGB) population of the Large Magellanic Cloud (LMC) by characterizing the individual sources in terms of the main properties of the progenitors and of the dust present in the circumstellar envelope. To this aim we compare the combination of the spectroscopic and photometric data collected by Spitzer, complemented by additional photometric results available in the literature, with results from AGB modelling that include the description of dust formation in the wind. To allow the interpretation of a paucity stars likely evolving through the post-AGB phase, we extended the available evolutionary sequences to reach the PN phase. The main motivation of the present analysis is to prepare the future observations of the evolved stellar populations of Local Group galaxies that will be done by the James Webb Space Telescope (JWST), by identifying the combination of filters that will maximize the possibilities of characterizing the observed sources. The present results show that for the M-star case the best planes to be used for this purpose are the colour magnitude ([F770W]-[F2550W], [F770W]) and (K-S-[F770W], [F770W]) planes. In these observational diagrams the sequences of low-mass stars evolving in the AGB phases before the achievement of the C-star stage and of massive AGBs experiencing hot bottom burning are clearly separated and peculiar sources, such as post-AGB, dual-dust chemistry, and iron-dust stars can be easily identified.