In human-computer interaction, understanding user behaviors and tailoring systems accordingly is pivotal. To this end, general-purpose user representation learning based on behavior logs is emerging as a powerful tool in user modeling, offering adaptability to various downstream tasks such as item recommendations and ad conversion prediction, without the need to fine-tune the upstream user model. While this methodology has shown promise in contexts like search engines and e-commerce platforms, its fit for instant messaging apps, a cornerstone of modern digital communication, remains largely uncharted. These apps, with their distinct interaction patterns, data structures, and user expectations, necessitate specialized attention. We explore this user modeling approach with Snapchat data as a case study. Furthermore, we introduce a novel design and evaluation framework rooted in the principles of the Measurement Process Framework from social science research methodology. Using this new framework, we design a Transformer-based user model that can produce high-quality general-purpose user representations for instant messaging platforms like Snapchat.