While applying favourites in the mobile app I noticed that the WebService is always returning false for isfavourite, when it shouldn't.

I debugged it and I've seen that, in core_message\api::get_conversation (used by the WebService), the context passed to favourite_exists is always 1 ($systemcontext). However, in the function set_favourite_conversation the context used is the conversation context. This causes the WS not to find the record and it thinks the conversation isn't favourite.