1&1 Domain Registration

So I sold a domain to someone but have kept the domain pointing to 1&1 nameservers at request of the new owner, the domain ownership has been transferred at Nominet and there is a new registrar.

Yesterday I got an invoice from 1&1 which included the ‘sold’ domain, I informed them they are not the registrar and to credit this item, they say;

“We would like to inform you that invoices raised prior to cancellation or transfer would still be valid invoice here on our system and still needs to be settled.”

Surely they can not charge for this domain registration fee when they are not the registrar? Can they?