The advent of modern technology has not only prompted the active presence of interest groups on social media but has also spurred their utilization of social media for a wide array of purposes, including lobbying. While recent scholarship has begun to unravel the prevalence and outcomes of such activities, there remains a gap in understanding the specific mechanisms through which groups advocate for their goals. Our study focuses on one such pivotal mechanism: the analysis of representative claims made by groups in the online sphere. Leveraging millions of tweets from the 2020-2022 period from organized interests in the US and multiple European countries, our focus is on understanding whose interests, values, or needs these groups claim to represent while advancing their lobbying messages. We start by using a classifier based on GPT-4 architecture to differentiate tweets serving advocacy purposes from those with other objectives. Thereafter, we train an additional classifier to explore on whose behalf or in whose interest different types of interest groups advocate. Our research sheds new light on the mechanisms driving lobbying in the online sphere by revealing how different types of interest groups use representative claims-making across policy issues and country contexts. This approach offers a novel perspective on understanding representation in the online sphere and holds implications for evaluating the role of organized interests in democratic governance.