o2 Homeboxes are exclusively lent or rented by o2 to the respective customer for use during the term of the contract. They always remain the property of o2 and must be returned to o2 at the end of the contract. The devices are assigned to the customer to whom they have been issued by o2 via the serial number. 
The transfer of the o2 Homebox to other persons and the operation at an address other than that agreed with o2 is not permitted. o2 Homeboxes that are not rented directly from o2 but have been obtained illegally will not be activated by o2. 

There is no legal way to buy an o2 homebox. 

Thanks. I think I'd like to hear that from someone who works at o2 though. There are TONS of Homeboxes on Kleinanzeigen, not from shady resellers but regular people, probably for a reason. I'm not sure what you mean by "o2 won't activate it" either. It's a matter of changing internal settings, isn't it?

When you ordered an o2 DSL connection, you confirmed that you had read and accepted the o2 terms and conditions/service description. Unfortunately, you obviously did not read them, otherwise you would know that the routers issued by o2 always remain the property of o2/Telefónica. Please take the opportunity now to at least read the relevant section. 

o2 AGB/Leistungsbeschreibung

Pflichten und Obliegenheiten des Kunden
Der Kunde ist verpflichtet, die Leistung sowie die bereitgestellten technischen Geräte ausschließlich an der vereinbarten Anschlussadresse zu nutzen.

Der Kunde darf Dritten ohne schriftliche Erlaubnis von Telefónica Germany den Anschluss sowie die zur Verfügung gestellten technischen Geräte nicht zur ständigen Alleinnutzung oder zur entgeltlichen Nutzung überlassen.

Optional bereitgestellte Router:
Soweit der Kunde die Bereitstellung eines Routers beauftragt hat, wird dieser dem Kunden für die Dauer des Vertragsverhältnisses zu Verfügung gestellt und verbleibt im Eigentum des Anbieters. Der Anbieter behält sich vor, überlassene Hard- und Software jederzeit zu aktualisieren. Nach Vertragsende oder nach Überlassung entsprechender neuer Hardware sind die Geräte vom Kunden auf eigene Kosten an den Anbieter zurückzusenden. 

If I take it from a "friendly perspective": The reason why o2 homeboxes are offered on ebay Kleinanzeigen is the same reason why you think you can buy them there: People don't read the contracts. 
If I take an "unfriendly perspective": People want to make money with stolen devices and they don't care if it is illegal or not. 

If, despite this, you are still thinking about buying an o2 Homebox via ebay, of which you now know at the latest that it is not the property of the seller but of o2: The purchase of stolen things is a criminal offence under §259 Strafgesetzbuch. 

o2 Homeboxes are configured exclusively via the o2 remote configuration. The operating menu does not contain any option for manual configuration. The o2 Homebox contacts the remote configuration server during installation and is not operated by this server if the device is assigned to another customer.
Since you have obviously not familiarised yourself with the range of functions and operation of an o2 Homebox 6641, I would recommend reading the manual. By the way, the operating menus of the o2 Homebox 6641/6441/6741 are exclusively in German. 

Thank you for your answer and warning me about the risks. That being said, I’ve gotten my answer elsewhere that they do in fact work even if they’re second-hand. I don’t really care if it’s not 1000% rules-abiding, to be totally honest. I know Germans love their rules and reminding others about them, but I’ll take my chances. If it doesn’t work, I’ll just get a Fritzbox.

By buying stolen goods, you immediately make a good impression in your host country, Germany. 

And I always wonder who buys all the stolen bikes: People without morals and respect for the law.

If they’re stolen goods, why is nothing done about them, legally-speaking? There are tons of them online. I never said I would “buy stolen goods” either, you have to calm down with your righteousness. I found a friend who has one lying around who offered to give it to me.

As you and your friend should know: This is not allowed. 

Thank you, message received. Let’s change the tone though, if you’re keen: which Fritzbox or modem model would you recommend for a My Home L plan? Looking for a cheap option that does the job.

That depends on which features are desired. 
If Wi-Fi is to be used, it certainly makes sense to have a device with support for the AC standard. 
7590, 7590AX, 7530, 7530AX, 7520, - these devices are future-proof due to support for VDSL supervectoring (profile 35b). 
7560 and 7490 should also work passably, but no 35b support. If no telephone is needed: 3490. 

The black Fritzboxes from 1&1 can also be used.

The serial number can be used to determine the date of manufacture of the Fritzboxes. In the case of newer Fritzboxes, ask for the original sales slip if possible, then you can make use of the 5-year AVM manufacturer's warranty. 

Thank you, I’ll have a look. Any other cheaper brand that would work?

Is Wi-Fi required and should a telephone set be connected?

Wi-Fi of course, phone no. I just need something basic that will do the job, and I find the Fritzboxes a bit expensive. 

The Speedport Smart series is sometimes available second-hand at a good price. However, the menu is probably in German and the range of functions is not as large as with the Fritzboxes. No manufacturer's warranty. 

Maybe also the Digitalisierungsbox Basic, have a look at ebay. However, the features and operation of the device are designed for business customers. 

Thanks! I’ll have a look. Hey, sorry to bother you with so many questions, but I’ve posted another, more pressing issue that I have with my activation. Would you be able to have a look? Basically, I’ve ordered on the 7th and haven’t received any “welcome letter”, contract, confirmation of anything. Customer service (in English and German) has zero clue what to do either. I just wanna make sure I actually have internet as ordered for mid-May.

Trying to get a confirmation from customer service about my upcoming DSL activation | O₂ Community (o2online.de)

Hi @gjolicoeur ,

as @blablup already explained. we can’t offer support for a homebox which was not sent you, I’m afraid. Regarding your connection itself: My co-workers will take a look as soon as possible; Please keep an eye on your thread regarding the acitivation and on your inbox.

Thanks for your answers and recommendations, @blablup !

Best regards,
Kurt