At first: In accordance to §46g (6) TKG (telecommunications law), you are allowed by law to prematurely end a telecommunications contract if the contractually agreed services cannot be fullfilled at your new location.
This usually only applies to landline contracts, as mobile contracts can be used anywhere, even abroad.
For landline contracts, it is irrelevant if moving inside Germany (or even inside a town) or if moving abroad - the only thing that matters is that the contractually agreed service cannot be fullfilled at the new address (whereever it is).
In order to take that right, you have to inform your provider (whomever it is - Vodafone but also other providers) that you move to a new location that is not served by your provider with the contractually agreed services. The provider may ask for an official document that prooves your move later on to check that you really did a relocation.
Anyhow, the 3 months notice period starts the earliest with the date you move - so even if you'd notice your provider (e.g. Vodafone) 3 months in advance to your move, the period is starting the earliest with your movement date. Anyhow - in case your movement announcement / relocation letter is sent AFTER you move, the 3 months will obviously start from the day that your letter is received by Vodafone.
And before you ask: Yes, it's indented by the law that you have to pay for (at least) 3 months after relocating - as a compensation for a contract that would otherwise run much longer. Because before this rule was adopted a few years ago, you would've been required by law to pay for the entire rest of the contractual term even if you could not receive any service as moving is considered as solely being in the responsibility of the consumer.
