  The paper continues the analysis, started in [1] (Part I,arXiv:2302.04353),
of the model open wave-guide problem defined by 2 semi-infinite, rectangular
wave-guides meeting along a common perpendicular line. In Part I we reduce the
solution of the physical problem to a transmission problem rephrased as a
system of integral equations on the common perpendicular line. In this part we
show that solutions of the integral equations introduced in Part I have
asymptotic expansions, if the data allows it. Using these expansions we show
that the solutions to the PDE found in each half space satisfy appropriate
outgoing radiation conditions. In Part III we show that these conditions imply
uniqueness of the solution to the PDE as well as uniqueness for our system of
integral equations.
