This technical note reports a simple, but effective strategy to derive a single coordinate transformation of a generic n-dimensional piecewise-linear continuous vector field that puts both of its subsystems into the same observer or control canonical form. The only hypothesis required is that both subsystems are either observable or controllable. To derive the result, the structure of the system is used in order to prove that it suffices to consider the same transformation for both subsystems. The theoretical results are illustrated by means of the Colpitts oscillator as a practical case of study.