This paper introduces a novel approach to providing continuous, personalized, and context-aware assistance through a Migratable Artificial Intelligence (mAI) system. The proposed idea is to enable a single intelligent agent to migrate across heterogeneous embodiments, such as social robots, tablets, and smart TVs, while preserving its identity, memory, and cognitive state. Designed in close collaboration with clinical professionals, the system will aim to address key needs within a long-stay rehabilitation unit, such as maintaining patient engagement during unstructured moments, supporting therapy adherence, and reducing the burden on clinical staff. A user-centered approach is introduced to conceive specific user requirements for a clinical scenario. The mAI system architecture relies on a shared ontological representation and a modular reasoning structure, allowing the intelligent agent to deliver personalised assistance across different stages and environments of care. The architecture is then applied in a simplified version to the selected case study. The resulting system also includes real-time integration of physiological data from wearable sensors and supports adaptive interventions through cognitive and physical training modules. A structured clinical study is identified to evaluate the viability of the system and its impact on motivation, activity, and emotional well-being.