Nowadays telecommunication operators which manage various network types are looking for convergence in different domains, from the access and aggregation to the core network. Moreover, in future 5G networks, the explosion of Internet of Things and the need of fixed and mobile convergence will imply strong requirements for more simplified and unified subscriber management. This will lead notably to seamless user experience when moving from a network to another. This paper proposes a pragmatic approach to operators for moving their networks smoothly to a really convergent subscriber data and session management system. It takes into account legacy mechanisms of subscriber management and introduces a universal Authentication, Authorization and Accounting (AAA) which aims at replacing progressively the legacy subscriber databases and helps in moving to a unified logical network element that will manage all subscriber's data and sessions. This paper illustrates the proposals with some use cases.