I purchased an iPhone 13 Pro Max yesterday and traded in my iPhone 12 Pro Max. Prior to trading in, I backed up the 12 to my iMac, in addition to doing nighty iCloud backups. The 12 was running iOS 15.1 very successfully.
The 13 won't accept a restore from the iMac because as received, the 13 has 15.0 installed. In the past whenever I have purchased a new iPhone, this problem was addressed by installing the Beta profile on the new phone, updating it to the latest beta, and then performing the restore. In the past it worked because the restore and the new (receiving) phone were both running the same beta version.
This time it is not working. I can install the Beta Profile on the new 13 Pro Max but when I start the 15.1 download process, before trying to restore from the iMac, I get an error stating that 15.1 cannot be downloaded to the 13. I've tried several workarounds including but not limited to wiping the 13 Pro Max and starting over, removing the SIM card and trying again, et cetera, but nothing is working.
As it stands, the new 13 Pro Max is not useful for me because I cannot get my apps and data transferred to it from my 12 Pro Max backup. I had to restore from that backup to an older iPhone XS Max with 15.1 on it to get a fully functional phone again. That backwards restore, from a 12 Pro Max running 15.1, to an XS Max running 15.1, worked.
This seems to be a bug with the 13 Pro Max. I would like to get my new phone up and running.
I was able to fix this problem. Actually, there were two problems.
The first problem was that Apple had not yet posted iOS 15.1 restore images (ipsw files) for the iPhone 13 Pro Max on the day that I tried to update my new phone, 24 September. Three days later, on 27 September, Apple did post those restore images.
Once the restore image, or ipsw file, became available on the developer site, I tried to download it to the phone using the over-the-air facility in the Settings app (General-->Software Update). This did not work; I got the same error. However, I was able to download the ipsw file using the iPhone management tool in Finder. Once downloaded, I could point Finder to the file on my Mac, and upgrade the phone that way, using a Lightning cable. After the phone was updated to 15.1, I was able to restore from a backup created from my iPhone 12 Pro Max before I traded it in.
All of this was a little troubling, but Apple does warn developers not to install beta software on primary devices. The phone is working well now.