This is not permitted. The customer may not allow third parties to use the connection or the technical equipment provided to him for permanent sole use or for use against payment.
The customer must inform Telefónica Germany immediately of any change of address.

There are two possibilities:
You order o2 to move the o2 DSL connection to your new address. You can then continue to use the service there. If the service cannot be provided by o2 at your new address, you may terminate the contract prematurely with a notice period of 3 months to the end of the calendar month. 

More to read: How to move your DSL connection to a new appartment

Move to another appartment- Can I cancel my current contract?

The second possibility is that you cancel the contract to the end of the term. o2 will technically shut down the connection and bill you for all remaining contract months at once. 

If you have received a router from o2, it must be returned at the end of the contract. If you do not return the rented router, o2 will charge you the value of the device. Please use the o2 DSL returns portal for the return.