IP multicast deployment recently progresses, but group services often remain restricted to limited domains and fail to comply with route-optimizing mobility management of the next generation Internet. Source Specific Multicast (SSM) facilitates transparent inter-domain routing and is expected to globally disseminate to many users and services. However, mobility support for Source Specific Multicast is still known to be a major open problem. In this paper, we propose the Enhanced Tree Morphing (ETM) protocol for extending SSM routing to mobile multicast sources. The scheme dynamically adapts SSM forwarding states to sender mobility, and transforms (morphs) source specific distribution trees into new, optimal trees rooted at a relocated source. ETM is simple, robust and secure, while it admits superior performance in packet forwarding at a low signaling overhead. Extensive evaluations based on a full protocol implementation, and simulations based on real-world topology data are performed, granting full insight into the properties of packet loss and delay stretch, protocol convergence times and router state evolution during single and rapidly repeated handovers. In a constant bit rate scenario, an ETM source handover typically leads to a slightly increasing delay of the first data packet, only. When operating on realistic network topologies, the protocol uniformly converges within less than 50 ms, thereby sustaining robustness under rapid source movement at all speeds common to our mobile world. Further optimizations are identified for FMIPv6 and for multihomed nodes.