My cousin did the same thing last year: got a new phone as a gift and left the old one in a drawer for months. When he finally checked the trade-in value, it still covered a decent chunk of his next upgrade. I'd say don't wait too long, since older models lose value fast. For a simple print-label-and-send process, I've seen people use
https://handyswap.com/de-en . You get a quote online, ship the device, and they handle the rest. Just make sure you back everything up and remove your accounts first, that saves headaches later.