Individuals frequently form deep attachments to physical objects (e.g., plush toys) that usually cannot sense or respond to their emotions. While AI companions offer responsiveness and personalization, they exist independently of these physical objects and lack an ongoing connection to them. To bridge this gap, we conducted a formative study (N=9) to explore how digital agents could inherit and extend the emotional bond, deriving four design principles (Faithful Identity, Calibrated Agency, Ambient Presence, and Reciprocal Memory). We then present the Dual-Embodiment Companion Framework, instantiated as Deco, a mobile system integrating multimodal Large Language Models (LLMs) and Augmented Reality to create synchronized digital embodiments of users' physical companions. A within-subjects study (N=25) showed Deco significantly outperformed a personalized LLM-empowered digital companion baseline on perceived companionship, emotional bond, and design-principle scales (all p<0.01). A seven-day field deployment (N=17) showed sustained engagement, subjective well-being improvement (p=.040), and three key relational patterns: digital activities retroactively vitalized physical objects, bond deepening was driven by emotional engagement depth rather than interaction frequency, and users sustained bonds while actively navigating digital companions' AI nature. This work highlights a promising alternative for designing digital companions: moving from creating new relationships to dual embodiment, where digital agents seamlessly extend the emotional history of physical objects.