Human smuggling networks are complex and constantly evolving, making them difficult to analyze comprehensively. Legal case documents offer rich factual and procedural insights into these networks but are often long, unstructured, and filled with ambiguous or shifting references, posing significant challenges for automated knowledge graph (KG) construction. Existing methods either overlook coreference resolution or fail to scale beyond short text spans, leading to fragmented graphs and inconsistent entity linking. We propose LINK-KG, a modular framework that integrates a three-stage, LLM-guided coreference resolution pipeline with downstream KG extraction. At the core of our approach is a type-specific Prompt Cache, which consistently tracks and resolves references across document chunks, enabling clean and disambiguated narratives for structured knowledge graph construction from both short and long legal texts. LINK-KG reduces average node duplication by 45.21% and noisy nodes by 32.22% compared to baseline methods, resulting in cleaner and more coherent graph structures. These improvements establish LINK-KG as a strong foundation for analyzing complex criminal networks.