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.
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