Other than creating a custom transaction, as suggested above, there is no way to add a query to Favorites, to my knowledge. There might be a way to shorten the query list within he group by applying a filter in the ALV layout (query list itself is an ALV grid), but that's about it.
It does seem though that the query user groups are not maintained very well in this case, perhaps it'd make sense to revise them to align with the user roles better. We use queries a lot, but only a few users even have access to more than one group, so this has never been an issue.
