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Patents are essential carriers of technological innovation, and their efficient transfer is critical for accelerating technological iteration in the lithium battery industry and supporting sustainability in the new energy sector. However, existing patent recommendation methods lack frameworks for handling heterogeneous enterprise demands, which limits the accuracy of supply–demand matching. This study proposes a knowledge graph-based differentiated patent recommendation framework for enterprise technological demands in the lithium battery domain. A five-element content framework—material, method, efficacy, product, and application—is constructed from both the supply and demand sides. Enterprise demands are classified into complete and incomplete types based on element coverage, and patent supply knowledge graphs are built for potentially relevant patents. Two differentiated recommendation methods are then developed. For complete demands, the Precision Recommendation Method for Complete Technological Demands integrates BERT-based semantic encoding, TransE-based structural modeling, and RAG-based constraint retrieval to achieve precise matching under full element coverage. For incomplete demands, the Fuzzy Recommendation Method for Incomplete Technological Demands incorporates multi-source enterprise data to enrich demand categories and constructs augmented query contexts to generate diversified candidate patent sets. Empirical validation based on 25 demand-driven patent transfer cases shows that the PR-CTD method exactly identifies the actual transferred patents in three cases. The FR-ITD method ranks 6 out of 14 actual transferred patents within the Top-5 results, while the remaining cases are all within the Top 13. These results demonstrate the effectiveness of the proposed framework in real-world patent transfer scenarios. This study provides a novel theoretical perspective for the structured modeling of heterogeneous technological demands and supply–demand semantic matching. It also offers practical value by improving the efficiency of patent retrieval and matching, thereby supporting patent technology transfer in the lithium battery industry.