This study explored how avatar face Level of Detail (LOD) and task types affect users' social presence and interpersonal communication in Augmented Reality remote collaboration. In AR remote collaboration, users are represented as avatars, and an actual user's appearance inevitably changes. While certain situations require an avatar that resembles a user, it is challenging to reconstruct everything realistically due to its high cost. Since facial parts show relative significance compared to body parts, we proposed controlling face LOD as an approach to lowering the cost while maintaining social presence in AR environments. Our results showed that while Mid-LOD maintains social presence but reduces costs compared to High-LOD, Low-LOD negatively impacts social presence mainly due to emotional understanding. Based on our findings, we highlight the importance of 1) considering facial expressions and emotional understanding in managing face LOD, 2) figuring out the collaboration context with different effects of tasks and communication behaviors, and 3) providing additional communication cues for maintaining social presence while lowering the cost.