Cross-domain recommendation is a core problem in content-to-e-commerce platforms. Its objective is to leverage user interactions with content to infer potential purchasing intent on the e-commerce side, thereby enhancing conversion rates and commercial value. However, in real industrial scenarios, cross-domain recommendation faces multiple challenges: significant semantic gaps exist between different domains, and user cross-domain behavior sequences are often massive in scale and rich in noise. Although large language models (LLMs) possess powerful semantic understanding and reasoning capabilities, their millisecond-level inference latency makes direct application in online recommendation systems difficult. To address these issues, this paper introduces AIR (Atomic Intent Reasoning), an LLM-driven cross-domain recommendation framework designed for industrial-grade deployment. By migrating LLM inference to the offline phase and dynamically constructing user intent representations through efficient retrieval and composition during online operations, it achieves approximately 400* inference acceleration while maintaining semantic consistency. Experimental results across multiple public datasets demonstrate that our method achieves state-of-the-art performance in cross-domain recommendation tasks. Furthermore, large-scale online A/B testing conducted in Kuaishou E-commerce's real-world business scenarios shows that our approach delivers stable and significant improvements across multiple core business metrics, including a +3.446% increase in GMV, fully validating its effectiveness and practical value in industrial-scale recommendation systems.