  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 (Ks-[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
