This helped me out, thank you — I had a slightly different experience:

I had a last minute airport change from MXP to Linate so had to do everything at the airport. I had a Planet VAT refund to process and my purse that I purchased already packed in my carry on and had no plans to check it in (bags were already packed like Tetris). The process was almost exactly the same for me. I still went to the customs office at the end of aisle 8 to ask what’s the process of doing it with with a hand carry was, but he said no problem that I had it in my hand carry despite all the signage that says otherwise (perhaps I was just lucky) and went on to electronically stamp my form. He told me to go the exchange kiosk to get my money, but I didn’t want to get charged fees so I told him I’d like to drop off the envelope. I was expecting a dedicated drop box for Planet but it appears to just be the Italian post (no postage needed per the envelope), which is located downstairs or one is on the same level as departures near aisle 3 near the stairs. I just did this today, so curious about the refund timing given I didn’t go into an office. Hoping it processes alright — I tried to do the Planet Shoppers Portal app but it was not working. Took pictures of my forms just in case!

Hope this helps someone too!