Large Language Models （LLMs） bring enhanced semantic understanding and personalized recommendation capabilities to recommender systems， however， they face significant challenges in user fairness in practical applications. The existing methods for LLM-based fair recommendation often rely on explicit sensitive attributes for constraints or reweighting， making them difficult to apply in scenarios where such attributes are unavailable due to privacy protection or inaccessibility. To address this issue， an FAIR recommendation framework for large language models with Sensitive Attribute Absence （FAIR-SAA） was proposed. In this framework， recommendation fairness was enhanced without accessing sensitive attributes through dynamic prompt optimization and adversarial reweighting. Specifically， in the first stage， a dynamic prompt optimization strategy was adopted to identify high-loss samples during the fine-tuning process， and these samples were utilized as contextual examples to mitigate stereotypical patterns； in the second stage， an adversarial reweighting mechanism was introduced to focus on underperforming regions of the model dynamically， thereby increasing the impact of underrepresented samples on model updates. Experimental results on three public datasets such as MovieLens-1M show that FAIR-SAA reduces the gender group Normalized Discounted Cumulative Gain NDCG@10 and Hit Ratio HR@10 by 74.47% and 61.76%， averagely， with a recommendation accuracy maintained comparable to baseline recommendation accuracy of the BI-step Grounding Paradigm for Recommendation （BIGRec）. When BIGRec is used as the base recommendation model， even when compared with Fairness-Aware Conformal Thresholding and Prompt EngineeRing （FACTER） framework， a fair recommendation method with full access to sensitive attributes， FAIR-SAA is competitive with 58.33% fairness metric. It can be seen that FAIR-SAA provides an effective solution to recommendation fairness problem in real-world privacy-preserving scenarios.