If you have concluded a contract with o2 with a fixed term, you must also fulfil it, i.e. pay for it, over the entire agreed term. The law does not provide for a general special right of termination in the event of a move. The legal regulation reads as follows:

Telekommunikationsgesetz (TKG)
§ 46 Anbieterwechsel und Umzug

Wird die Leistung am neuen Wohnsitz nicht angeboten, ist der Verbraucher zur Kündigung des Vertrages unter Einhaltung einer Kündigungsfrist von drei Monaten zum Ende eines Kalendermonats berechtigt.

The check whether this legal requirement is met is carried out within the process of a removal order.
If you do not wish to give a removal order to o2, you can only terminate the contract with effect to the end of the agreed contract term. You will then be billed by o2 for the remaining contract months. 

Thanks @blablup for the prompt reply. I wish to issue a removal order.

Does O2 provide a form? Is there any form for my particular case?

Is the address “Telefónica Germany GmbH & Co. OHG // Kundenbetreuung // 90345 Nürnberg”?

Best,

You can try the online form (Mein o2) or contact customer service (recommended). 

https://www.o2online.de/service/internet-umzug/

If you are asked for data of previous tenants, don’t give any. 

I chatted with an O2 operator. For whom it may concern, at this time, here follows the info I gathered:

• there is no specific form;
• you can write this letter in English (although, as a personal opinionated suggestion, I would go for German with an automatic translator);
• the address is still the same: Telefonica Germany GmbH & Co. OHG Kundenbetreuung, 90345 Nürnberg;
• subject "Sonderkündigung" (it means “special/extraordinary cancellation”, it is the removal order);
• provide your name, your phone number, your client number, your old and new address, and a brief extraordinary reason for the removal order;
• also provide proof of your reason: in my case, I’ll provide as attachment the “Wohnungsgeberbescheinigung” (the certification of your “accommodation provider”, i.e. your friend or renter) and their previous DSL contract. These documents will help the operators to understand your case.

I provide this information “as is”, with NO WARRANTY, NO LIABILITY. I write them just as guidelines to find your own solution for your own case/s. In particular, “the check whether this legal requirement is met is carried out within the process of a removal order”, as written above.

Hope it will help someone.

Best,

We look forward to hearing back if your request was successful. Experience shows that goodwill requests are usually rejected. Any reason that is no specified by German law is irrelevant. “Moving into a flat where already is an DSL connection” is not mentionend in §46 TKG as a valid reason and therefore it is very likely that your request for “special cancellation” will be denied.

“Sonderkündigung” is NO removal order! Removal order means that you ask o2 to move your o2 DSL connection to a new address. If you move out of your old flat, o2 is obliged to shut down the connection. If the customer does not issue a removal order, the remaining term is calculated. 

You should make sure that you specifically request that the connection be moved if possible, otherwise if o2 determines that the conditions for early termination are not met (because o2 can provide the service at your new address) the connection at your old address will simply be deactivated and you will be billed for the rest of the contract term. You may if course prefer that option as it saves you the fee for moving the connection if you do not really need it.

@blablup

A removal order is actually relevant to an Abschiebung  It is clear what you meant but the Umzugsauftrag here is in fact a request to move the broadband connection. Just FYI.

Gut, dann schreibe ich fortan immer Umzugsauftrag. Sollen doch die Englischsprecher sich selbst die passende Übersetzung heraus suchen. Wenn ich ein nicht ganz treffsicheres Übersetzungsprogramm nutzen kann, können das englischsprechende Personen sicherlich auch. 

Deepl ist normalerweise ziemlich gut (viel besser als Google Translate), aber ohne Kontext sind die Ergebnisse nicht immer passend. Auftrag ist sowieso schwer ins Englische zu übersetzen.

Das sollte übrigens nur ein Hinweis und keine Kritik sein, falls du den Kommentar als Kritik aufgefasst haben solltest.

Was ist denn nun deiner Meinung nach die korrekte Übersetzung für Umzugsauftrag? Mir fallen auch ehrlich gesagt gar keine anderen Kontexte für “Umzugsauftrag” ein. 

Das kommt darauf an was umgezogen wird. Wird z.B. ein Telefonanschluss umgezogen 'request to move / transfer the broadband / telephone connection.' Wenn man z.B. eine Umzugsfirma mit dem Transport von Möbeln usw. beauftragt, dann wäre removal nicht falsch, aber nicht order sondern booking. - to book or arrange a furniture removal.

Ich bleibe einfach bei Umzugsauftrag, wenn es anscheinend keine Übersetzung sondern nur eine Umschreibung gibt. 

I have to send the router back. Which is the address?

I you return the route now, you can not use it anyone in the case that your goodwill request will be rejected. 

I would therefore recommend that you wait until you have received a written decision from o2 regarding your cancellation request before you return the letter. 

Otherwise, you can find all information on the topic of returns on the o2 website:
https://www.o2online.de/service/retoure/

"Wird die Leistung am neuen Wohnsitz nicht angeboten" → Can O2 offer the service in the new place of residence where there is another telecommunication company (already providing DSL)? I guess no.

@bs0 : what is your take on this?

What you guess is irrelevant. Do what you want, but don't complain about the result afterwards. 

In deed, the fact that another provider offers DSL there is a good indication that o2 can do the same. 

Yes, they probably can. It is technically possible to have two DSL connections at the same address. That is why there is no automatic right to terminate the contract early in such cases.

OK thank you both for the answers. @bs0@blablup