The router ends with your contract, but it was never yours. If you don't send it back they'll bill you what a new one costs, usually somewhere between eighty and two hundred and fifty euros.
Telekom sends a return label along with the cancellation confirmation, and you can generate one online or hand the thing in at a shop. Vodafone wants their hardware back within fourteen days of the contract ending, at your cost.
We ask for the label in the letter itself, so it turns up while you're still in Germany and can walk to a post office.
A rented device often has its own minimum term, separate from your tariff. If you end it early there may be a payment for the remaining months, and the amount only appears on the cancellation confirmation.
We read the terms per contract reference straight off your invoice, so if a device runs longer than the main contract you hear about it before you decide anything.
A phone on monthly instalments is a purchase, not a rental. It survives the cancellation and the phone is yours. Mixing the two up either has you posting back something you own, or leaving a balance running you thought was settled.