You don't have to as the CNBC will forward it. However, you don't know when they will do that. There is no harm in sending a copy to the claimant or their solicitor, if they're using one. You will have to copy them in for any future filing though, such as when you file your N180 DQ and when you submit your WS.
When submitting anything to more than one party, you should use a single email with all the required recipients in the main address field and also CC in yourself. That way, if one party receives it and you don't get any bounce-back error messages, they all received it. As to whether the correct person received it is different matter but the same would apply to something sent by post. You rely on whoever opens the post to make sure that the correct person/department receives the communication.
Your copy is the easy proof of posting although there will be forensic level evidence as proof of posting in the email headers anyway.
