  Using the intrinsic PSR J1903+0327 parameters evaluated from radio
observations (mass, rotation period and dipole magnetic field deduced from the
timing properties) we calculate the mass of its neutron star progenitor, M_i,
at the onset of accretion. Simultaneously, we derive constraints on average
accretion rate Mdot and the pre-accretion magnetic field B_i. Spin-up is
modelled by accretion from a thin disk, using the magnetic-torque disk-pulsar
coupling model proposed by Kluzniak and Rappaport (2007), improved for the
existence of relativistic marginally-stable circular orbit. Orbital parameters
in the disk are obtained using the space-time generated by a rotating neutron
star in the framework of General Relativity. We employ an observationally
motivated model of the surface magnetic field decay. We also seek for the
imprint of the poorly known equation of state of dense matter on the spin-up
tracks - three equations of state of dense matter, consistent with the
existence of 2 Msun neutron star, are considered. We find that the minimum
average accretion rate should be larger than 2-8 10^(-10) Msun/yr, the highest
lower bound corresponding to the stiffest equation of state. We conclude that
the influence of magnetic field in the "recycling" process is crucial - it
leads to a significant decrease of spin-up rate and larger accreted masses, in
comparison to the B=0 model. Allowed B_i-dependent values of M_i are within
1.0-1.4 Msun, i.e., much lower than an oversimplified but widely used B=0
result, where one gets M_i>1.55 Msun. Estimated initial neutron-star mass
depends on the assumed dense-matter equation of state.
