Multi-modal imbalanced cross-source entity alignment aims to identify equivalent entity pairs across multi-modal knowledge graphs (MMKGs) that encompass diverse data sources with imbalanced modality, which poses significant challenges due to the non-uniform distribution of information across different modalities. Existing methods encounter major limitations in aligning entities across MMKGs, where missing data and modality-specific inconsistencies thus create information gaps. These gaps, stemming from disparities in neighborhood structure and attribute availability, result in reduced alignment performance. To address these challenges, we propose a novel multi-modal fact knowledge generation framework to advance imbalanced cross-source entity alignment. Utilizing large language models (LLMs) for comprehensive knowledge completion, our framework enriches MMKGs by synthesizing missing neighboring entities and relational attributes, enabling precise one-to-one similarity comparisons across all relations and attributes. Specifically, neighbor entity completion generates probable neighboring entities to fill structural gaps, while attribute completion synthesizes missing relational attributes to improve alignment. The facts evaluation module assesses generated triples, ensuring that only high-quality information supports the alignment. Extensive experiments on benchmark datasets demonstrate that our framework significantly outperforms strong competitors, achieving superior entity alignment performance.