This work is the sequel to Continuous Quivers of Type A (I). In this paper we define the Auslander-Reiten space of a continuous type quiver, which generalizes the Auslander-Reiten quiver of type quivers. We prove that extensions, kernels, and cokernels of representations of type can be described by lines and rectangles in a way analogous to representations of type . We provide a similar description for distinguished triangles in the bounded derived category whose first and third terms are indecomposable. Furthermore, we provide a complete classification of Auslander-Reiten sequences in the category of finitely generated representations of . This is part of a longer work; the other papers in this series are with Kiyoshi Igusa and Gordana Todorov. The goal of this series is to generalize cluster categories, clusters, and mutation for type quivers to continuous versions for type quivers. (Added Section 5 to version 2.)