Every non-trivial distributed application needs to exchange information in order accomplish its task, and reliable communication primitives are fundamental in failures prone distributed systems to guarantee correct message exchanges between parties. Their implementation becomes particularly challenging when considering distributed systems where processes are arranged in a multi-hop network and each of them may temporary and continuously be compromised by an attacker during the execution. Although some fundamental problems (such as the register implementation and the agreement) were investigated considering Mobile Byzantine Faults (MBF), most of the contributions consider a fully connected communication network. In this paper we analyze the specific difficulty of ensuring reliable communication between parties in a distributed system affected by Mobile Byzantine Faults (compared to the case where the Byzantine failures are static), showing that such a problem is essentially impossible to solve in asynchronous systems with MBF, and we propose a synchronous protocol providing reliable communication both in complete networks and specific multi-hop topologies.