You should get an email from Verizon when they inspect the phone. you can also go here: Check Electronic Device Recycling Status – Verizon Wireless and enter the submission ID you received in your trade in acknowledgement email to get status.
My trade-in was delivered on 10/4 according to the tracking label. When I check on the status it tells me that the recycling box was mailed- so it doesn't look like they have acknowledged the receipt yet. How long does it take?
I was told it could take a few days. Mine was delivered on 10/3 and mine shows the same "box mailed" message. They gave me their number to the trade in dept. Where I could call for more info. That number is : 1-800-416-8894. I haven't called yet, but I may Monday. I have another trade in to send but I'm not sending until my first one is processed. I have about three weeks before the second has to be sent. Hopefully this should give them plenty of time to check in the first one. You have to remember though they probably have a lot to go through as many took this offer.
Mine still shows Verizon received my phone for about a week now. Still doesn't show if the $650 appraisal value has been accepted but I suppose they probably have tons of phones to check.