Personalization in Large Language Models (LLMs) often relies on user-specific soft prompts. However, these prompts become obsolete when the foundation model is upgraded, necessitating costly, full-scale retraining. To overcome this limitation, we propose the Prompt-level User Migration Adapter (PUMA), a lightweight framework to efficiently migrate personalized prompts across incompatible models. PUMA utilizes a parameter-efficient adapter to bridge the semantic gap, combined with a group-based user selection strategy to significantly reduce training costs. Experiments on three large-scale datasets show our method matches or even surpasses the performance of retraining from scratch, reducing computational cost by up to 98%. The framework demonstrates strong generalization across diverse model architectures and robustness in advanced scenarios like chained and aggregated migrations, offering a practical path for the sustainable evolution of personalized AI by decoupling user assets from the underlying models.