With the rise of Large Language Models (LLMs), notably characterized by GPT frameworks, there emerges a catalyst for novel healthcare applications. Earlier iterations of chatbot caregivers, though existent, have yet to achieve a dimension of human-like authenticity. This paper unveils `MemoryCompanion' a pioneering digital health solution explicitly tailored for Alzheimer's disease (AD) patients and their caregivers. Drawing upon the nuances of GPT technology and prompt engineering, MemoryCompanion manifests a personalized caregiving paradigm, fostering interactions via voice-cloning and talking-face mechanisms that resonate with the familiarity of known companions. Using advanced prompt-engineering, the system intricately adapts to each patient's distinct profile, curating its content and communication style accordingly. This approach strives to counteract prevalent issues of social isolation and loneliness frequently observed in AD demographics. Our methodology, grounded in its innovative design, addresses both the caregiving and technological challenges intrinsic to this domain.