If you move to an area that is not served, you have a special right of termination according to §46 TKG, but with a period of 3 months from the date of the move, i.e. the provider will charge you the basic price for another 3 months.
Send an email to kundenservice@unitymedia.de with your customer data (customer number, name and address of the contract holder) and also write in when you are moving. You will then receive a confirmation of termination for the regular end of the contract. If you have the official de-registration certificate, submit it immediately and the cancellation will be put on the correct date. You send the cable router back with the package label enclosed with the cancellation confirmation within 14 days of the end of the contract (or in your case probably when moving). Please keep the delivery receipt and keep it so that you can prove the return in case something should happen (e.g. device did not arrive).
