The integration of Environmental, Social, and Governance (ESG) factors into corporate decision-making is a fundamental aspect of sustainable finance. However, ensuring that business practices align with evolving regulatory frameworks remains a persistent challenge. AI-driven solutions for automatically assessing the alignment of sustainability reports and non-financial disclosures with specific ESG activities could greatly support this process. Yet, this task remains complex due to the limitations of general-purpose Large Language Models (LLMs) in domain-specific contexts and the scarcity of structured, high-quality datasets. In this paper, we investigate the ability of current-generation LLMs to identify text related to environmental activities. Furthermore, we demonstrate that their performance can be significantly enhanced through fine-tuning on a combination of original and synthetically generated data. To this end, we introduce ESG-Activities, a benchmark dataset containing 1,325 labelled text segments classified according to the EU ESG taxonomy. Our experimental results show that fine-tuning on ESG-Activities significantly enhances classification accuracy, with open models such as Llama 7B and Gemma 7B outperforming large proprietary solutions in specific configurations. These findings have important implications for financial analysts, policymakers, and AI researchers seeking to enhance ESG transparency and compliance through advanced natural language processing techniques.