One-way wave extrapolators, such as the split-step Fourier method, generalized screen methods including the phase- screen, complex screen and wide-angle pseudo-screen methods, have been proposed recently as part of the solution to lessen the CPU and memory size requirement of wave equation based 3D subsurface imaging methods. The phase space path- integral formulation and the vertical slowness symbol analysis provide a general and convenient background for accuracy estimation and improvement of screen propagators. In this paper we review and elucidate the relevant theory and formulation in paper I (de Hoop and Wu, 1996), and present the results of accuracy analysis and numerical tests for screen propagators. By comparing the dispersion relations of screen propagators in the high-frequency limit with the leading term high-frequency asymptotics to the vertical slowness symbol, and through numerical experiments of thin-slab transmission, it is seen that for weak perturbations both the phase-screen and the wide-angle pseudo-screen propagators perform well; while for the case of strong medium contrasts, the modified wide-angle pseudo- screen propagator has much better accuracy for large-angle waves than the phase screen propagator. Unlike the traditional phase screen propagator which is purely a space domain operator, the wide-angle pseudo-screen propagator is a dual-damain operator. The screen propagators have great potential in the application to 3D prestack depth migration/inversion as extrapolators.