Very simple: Write the cancellation notice in German and request the cancellation to the end of the contractual term. You can either use regular mail to send it to the Erfurt postal address -or- you can use the contact form on your Cable self-service portal.
Next thing: Moving might be a reason for a premature cancellation, but only if the contract cannot be fulfilled as agreed upon, e.g. if your speed cannot be reached at the new location. It does not matter if there is already another line available or not - it only matters if your contract can technically be fulfilled. In either way, you'll need to provide your new address to Vodafone and ask for a relocation of the service (as you are not allowed to especially use the telephony service at another location than contractually agreed upon due to law requirements). In the case the contract cannot be fulfilled at your new (current) location, the contract can be cancelled prematurely with a 3 months notice period starting by the movement date but the earliest by the date you send the relocation request. So in your case, even if the contract cannot be fulfilled at your new address, the 3 months will the earliest start by the moment that your cancellation/relocation request including official proof is received by Vodafone - and you'll have to pay for 3 additional moths from that day on (so at least until mid of June in case you'd request the relocation/cancellation right now).
