Cross-platform recommendation (CPR) attracts increasing attention as a solution to data sparsity by leveraging non-overlapping user/item information from different platforms with similar services. Existing CPR methods face two main challenges: (1) the divergence in item IDs and content and (2) the divergence in user preference distributions across platforms. To tackle these challenges, we propose a CPR framework based on User and Item Prototype Alignment (UIPA). For item representations, UIPA constructs a unified item semantic space via a large language model (LLM) and aligns item prototypes across platforms. For user representations, UIPA aligns homogeneous groups through user prototype alignment and enhances platform unique groups with a pseudo-prototype generation strategy. UIPA is a plug-and-play framework, and experimental results on three pairs of datasets demonstrate that UIPA significantly improves the performance of different backbones on both source and target platforms.