In this paper, we study the solvability of fair exchange in the context of Byzantine failures. In doing so, we first present a generic model with trusted and untrusted processes, and propose a specification of the fair exchange problem that clearly separates safety and liveness, via fine-grained properties. We then show that the solvability of fair exchange depends on a necessary and sufficient topological condition, which we name the reachable majority condition. The first part of this result, i.e., the condition is necessary, was shown in a companion paper and is briefly recalled here. The second part, i.e., the condition is sufficient, is the focal point of this paper. The correctness proof of this second part consists in proposing a solution to fair exchange in the aforementioned model.