What do you mean firmware update? I'm assuming that's different than an iOS update based on how you are describing it? He is on the latest OS for his device, iOS 6.1.6 on the iPod Touch 4th generation. I tried to get him to do a full restore and he doesn't want to lose his stuff, even though he doesn't have much. Apparently it's not worth having a really convenient, smooth, reliable messaging service built in, that you can easily share stuff with.
Right now we have to use Skype and it is less than ideal. Me and 3 other friends are collaborating lately on something and this "gap" is extremely inconvenient, I find it very annoying he is unwilling to restore because it now is obvious it is an issue with his particular device. Does iTunes backup App Data and photos? I wonder if a backup->factory reset->restore from backup could clear things up? I already got him to do a "Reset All Settings" which was painful enough and it fixed nothing. I really find it annoying when casual users simply will not restore their device as new when they have serious issues that can't be fixed otherwise, why would you want to do that to yourself just for progress in a couple games? #
iTunes does back up everything, absolutely everything. Photos, the exact time you watered your plants last year, you name it, iTunes'll back it up. That could potentially work. To do a firmware update, do what I said about connecting the iPod to iTunes, and then click update, rather than restore. This should update firmware. I think. But if not, if it says that it's all up to date, restore it. An update this way will erase the iPod, so again, back up first!
P.S: after you've done this back up, go to the iTunes preferences, Devices, and you'll see all of the backups. Find the one you just did, right click it, and then click archive. This will make is a separate backup, and it's just easier to restore to.
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Caution though! If iTunes says that there is an update, DO NOT ARCHIVE THE BACKUP. Archived backups aren't compatible with new software as far as I'm aware, and the data will be lost forever. If this happens, and you have the iPod in Recovery Mode, disconnect it from iTunes, and hold down the home and power buttons until it turns off and on again, and the Apple logo appears.