You don't need to create both cross links. One cross link from the external entity is sufficient.
So you can create the role within your circle called “Cross Link from entity” and then add accountabilities on it as tension arises. This Cross Link will represent the whole external entity.
However, they cannot process tensions from your circle to their organization, it is only a one way - for that, you would need to do it differently as they don't practice Holacracy, you can't create another cross link.