Although Multi-Access Edge Computing (MEC) has evolved into a key technology for provisioning mobility-oriented and delay-sensitive applications, the storage and computing power limitations of user-end MEC devices still present a significant challenge in guaranteeing low latency in content delivery. When the requested content is out of the caching scope of local devices, effectively caching user-requested content with low cost and high hit rate has become a widely acknowledged research hotspot. Traditional caching strategies inadequately address the challenges posed by mobility and runtime variations in content popularity. In this work, we propose a personalized mobility-aware caching method (MAPHC) that synthesizes a content suitability prediction algorithm (CSPA) for identifying the caching needs of edge servers and a multi-agent deep reinforcement learning model for dynamically adjusting user mobility-aware caching strategies. Simulation results clearly demonstrate that MAPHC outperforms its peers across multiple performance metrics.