Millisecond pulsars (MSPs) are generally believed to be old neutron stars (NSs), formed via type Ib/c core-collapse supernovae (SNe), which have been spun up to high rotation rates via accretion from a companion star in a low-mass X-ray binary (LMXB). In an alternative formation channel, NSs are produced via the accretion-induced collapse (AIC) of a massive white dwarf (WD) in a close binary. Here we investigate binary evolution leading to AIC and examine if NSs formed in this way can subsequently be recycled to form MSPs and, if so, how they can observationally be distinguished from pulsars formed via the standard core-collapse SN channel in terms of their masses, spins, orbital periods and space velocities. Numerical calculations with a detailed stellar evolution code were used for the first time to study the combined pre- and post-AIC evolution of close binaries. We investigated the mass transfer onto a massive WD in 240 systems with three different types of non-degenerate donor stars: main-sequence stars, red giants, and helium stars. When the WD is able to accrete sufficient mass (depending on the mass-transfer rate and the duration of the accretion phase) we assumed it collapses to form a NS and we studied the dynamical effects of this implosion on the binary orbit. Subsequently, we followed the mass-transfer epoch which resumes once the donor star refills its Roche lobe and calculated the continued LMXB evolution until the end. We demonstrate that the final properties of these MSPs are, in general, remarkably similar to those of MSPs formed via the standard core-collapse SN channel. However, the resultant MSPs created via the AIC channel preferentially form in certain orbital period intervals. Finally, we discuss the link between AIC and young NSs in globular clusters. Our calculations are also applicable to progenitor binaries of SNe Ia under certain conditions. [Abridged]
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