In this paper we present the design and implementation of a Time Management Converter (TiMaC) for HLA based simulation systems. TiMaC is a layer interposed in between the federate and the underlying RTI in order to map the conservative Time Management interface onto the optimistic one. In this way, TiMaC transparently supports optimistic execution for federates originally designed for the conservative approach, which is achieved without the need for developing any ad-hoc RTI system. TiMaC relies on a recently proposed software architecture for transparent treatment of checkpointing/recovery of the federate state, namely Magic State Manager (MASM), and implements a set of additional facilities required to support all the tasks associated with the mapping of conservative onto optimistic Time Management interfaces. The implementation has been tailored to the Georgia Tech B-RTI package, although the underlying design principles would allow it to be integrated with any RTI system. We also report an experimental study demonstrating the viability and effectiveness of our proposal in allowing conservative federates to be supported with highly increased run-time effectiveness in general contexts for what concerns the features of the underlying computing systems (e.g. LAN vsWAN based systems.