The Escalator Boxcar Train (EBT) numerical method has been designed and widely used by theoretical biologists to compute solutions of one-dimensional structured population models of McKendrick-von Foerster type. Recently the method has been derived for age-structured two-sex population model (Fredrickson-Hoppensteadt model), which consists of three coupled hyperbolic partial differential equations with nonlocal boundary conditions. The convergence of the EBT method for Fredrickson-Hoppensteadt model has not been analysed, and relevant numerical examples are still missing. In this paper, we derive a simplified EBT method for the "two-sex model", and prove its convergence. However due to the interest in tracking specified cohorts of individuals, the analytical results cannot be analysed in L1 norm. Instead we embedded the problem in the space of nonnegative Radon measures equipped with the bounded Lipschitz distance (flat metric). We also present numerical examples to illustrate the results, compute the error in bounded Lipschitz distance and compare it against the total variation (TV) distance.