Large language models (LLMs) have been widely adopted to enrich the semantic representation of textual item information in recommender systems. However, existing linear autoencoders (LAEs) that incorporate textual information rely on sparse word co-occurrence patterns, limiting their ability to capture rich textual semantics. To address this, we propose L3AE, the first integration of LLMs into the LAE framework. L3AE effectively integrates the heterogeneous knowledge of textual semantics and user-item interactions through a two-phase optimization strategy. (i) L3AE first constructs a semantic item-to-item correlation matrix from LLM-derived item representations. (ii) It then learns an item-to-item weight matrix from collaborative signals while distilling semantic item correlations as regularization. Notably, each phase of L3AE is optimized through closed-form solutions, ensuring global optimality and computational efficiency. Extensive experiments demonstrate that L3AE consistently outperforms state-of-the-art LLM-enhanced models on three benchmark datasets, achieving gains of 27.6% in Recall@20 and 39.3% in NDCG@20. The source code is available at https://github.com/jaewan7599/L3AE_CIKM2025.