A Fog radio access network is considered as a network architecture candidate to meet the soaring demand in terms of reliability, spectral efficiency, and latency in next generation wireless networks. This architecture combines the benefits associated with centralized cloud processing and wireless edge caching enabling primarily low-latency transmission under moderate fronthaul capacity requirements. The F-RAN we consider in this paper is composed of a centralized cloud server which is connected through fronthaul links to two edge nodes serving two mobile users through a Z-shaped partially connected wireless network. We define an information-theoretic metric, the delivery time per bit (DTB), that captures the worst-case per-bit delivery latency for conveying any requested content to the users. For the cases when cloud and wireless transmission occur either sequentially or in parallel, we establish coinciding lower and upper bounds on the DTB as a function of cache size, backhaul capacity and wireless channel parameters. Through optimized rate allocation, our achievability scheme determines the best combination of private, common signalling and interference neutralization that matches the converse. Our converse bounds use subsets of wireless, fronthaul and caching resources of the F-RAN as side information that enable a single receiver to decode either one or both users' requested files. We show the optimality on the DTB for all channel regimes. In case of serial transmission, the functional DTB-behavior changes at fronthaul capacity thresholds. In this context, we combine multiple channel regimes to classes of channel regimes which share the same fronthaul capacity thresholds and as such the same DTB-functional. In total, our analysis identifies four classes; in only three of those edge caching and cloud processing can provide nontrivial synergestic and non-synergestic performance gains.