As users interact with more and more computing devices in daily life, there is strong need for the ability to move active sessions from one device to another -which is called session mobility. However, due to the complexity and range of devices in use today, providing such a solution poses significant challenges and many existing approaches fail to recognise this diversity among devices and platforms. We present our approach to session mobility which enables the mobility of platform independent legacy applications in an adaptive manner across a wide range of devices from the desktop computer to the smartphone. Providing such interaction continuity can help alleviate the cumbersome task of manually reinstating sessions on each device encountered, as well as enabling device integration and information centralisation. We discuss the design and implementation issues associated with our system, as well as presenting our test results in comparison to similar approaches to session mobility, thereby demonstrating the advantages of our approach.