An IP PBX system that serves enterprise telephones via a landline IP network connection is be expanded to serve cellular wireless communication devices (WCD) via a cellular wireless carrier's radio access network (RAN). Calls to and from the cellular WCD are connected through the cellular carrier's RAN and the IP PBX system, so that the IP PBX system can control and manage the calls just as the IP PBX would control and manage calls involving other extensions on the IP PBX. A cellular WCD thereby becomes an IP PBX client station, i.e., an extension on the IP PBX system. As such, the cellular WCD can seamlessly benefit from many of the same IP PBX features that other more conventional IP PBX client stations (e.g., desk phones) enjoy.