McLaughlin et al. discovered a drifting sub-pulse phenomenon in the radio emission of PSR J0737-3039B (B) caused by electromagnetic radiation from PSR J0737-3039A (A). Here we describe a geometrical model which predicts the delay of B's sub-pulses relative to A's radio pulses. As we demonstrate, this technique provides a new way of timing A's radio pulses from the point of view of an hypothetical observer located at B. We detail three astrophysical applications of measuring these delays: (a) to determine the sense of rotation of A relative to its orbital plane; (b) to estimate where in B's magnetosphere the radio sub-pulses are generated and (c) to provide an independent estimate of the mass ratio of A and B. The latter might improve existing tests of gravitational theories using this system.