There's no need to appeal yet. With "punishment order" they probably refer to a german "Strafbefehl" which isn't a full sentence but a simplified system to avoi

There's no need to appeal yet. With "punishment order" they probably refer to a german "Strafbefehl" which isn't a full sentence but a simplified system to avoid trials which only requires a bit more than probable cause. They can now object to it, then there will be a full trial. If they loose there, then they can appeal.