Evolutionary scenarios suggest that the progenitor of the new binary pulsar J0737-3039B was a He star with M > (2.1-2.3)M⊙. We show that this case implies that the binary must have a large (>120 km/s) center of mass velocity. However, the location, ∼50 pc from the Galactic plane, suggests that the system has, at high likelihood, a significantly smaller center of mass velocity and a progenitor more massive than 2.1M⊙ is ruled out (at 97% C.L.). A progenitor mass around 1.45M⊙, involving a new previously unseen gravitational collapse, is kinematically favored. The low mass progenitor is consistent with the recent scintillation based velocity measurement of 66 ± 15 km/s and rules out the high mass solution at 99% C.L. Conversely, if the unlikely higher mass solution is the true one we should increase the estimated rate of neutron star mergers by a factor of at least 2.