The widespread use of Environmental, Social, and Governance (ESG) communication on social media has enabled companies to convey sustainability promises to various stakeholders effectively. Yet it has also intensified greenwashing, characterised by false or unverifiable ESG announcements that distort public opinion and undermine trust in sustainability transitions. The extant literature offers limited tools or frameworks for measuring and identifying fake ESG claims. This paper proposes a scalable, AI-based framework for identifying fake ESG claims and greenwashing on social media. The proposed framework involves a multimodal architecture that uses transformer-based Natural Language Processing (NLP) of textual ESG claims, vision models for image-text consistency analysis, and social network analytics of coordinated amplification patterns. The study's significant contribution is evidence that combining linguistic, visual, and network indicators can enhance the detection of deceptive ESG narratives across industries. The suggested framework offers guidance to regulators, investors, and social media platforms interested in automated means to verify sustainability claims and limit harm.