  The already proved Lum-Chua's conjecture says that a continuous planar
piecewise linear differential system with two zones separated by a straight
line has at most one limit cycle. In this paper, we provide a new proof by
using a novel characterization for Poincar\'e half-maps in planar linear
systems. This proof is very short and straightforward, because this
characterization avoids the inherent flaws of the usual methods to study
piecewise linear systems (the appearance of large case-by-case analysis due to
the unnecessary discrimination between the different spectra of the involved
matrices, to deal with transcendental equations forced by the implicit
occurrence of flight time, ...). In addition, the application of the
characterization allow us to prove that if a limit cycle exists, then it is
hyperbolic and its stability is determined by a simple relationship between the
parameters. To the best of our knowledge, the hyperbolicity of the limit cycle
and this simple expression for its stability have not been pointed out before.
