  We study the evolution of close binary systems in order to account for the
existence of the recently observed binary system containing the most massive
millisecond pulsar ever detected, PSR J0740+6620, and its ultra-cool helium
white dwarf companion. In order to find a progenitor for this object we compute
the evolution of several binary systems composed by a neutron star and a normal
donor star employing our stellar code. We assume conservative mass transfer. We
also explore the effects of irradiation feedback on the system. We find that
irradiated models also provide adequate models for the millisecond pulsar and
its companion, so both irradiated and non irradiated systems are good
progenitors for PSR J0740+6620. Finally, we obtain a binary system that evolves
and accounts for the observational data of the system composed by PSR
J0740+6620 (i.e. orbital period, mass, effective temperature and inferred
metallicity of the companion, and mass of the neutron star) in a time scale
smaller than the age of the Universe. In order to reach an effective
temperature as low as observed, the donor star should have an helium envelope
as demanded by observations.

Solar and Stellar Astrophysics;High Energy Astrophysical Phenomena