  Freyd's Generating Hypothesis is an important problem in topology with deep
structural consequences for finite stable homotopy. Due to its complexity some
recent work has examined analogous questions in various other triangulated
categories. In this short note we analyze the question in noncommutative stable
homotopy, which is a canonical generalization of finite stable homotopy. Along
the way we also discuss Spanier--Whitehead duality in this extended setup.
