iPhone Backup – How iPhone Backup Extraction Programs Work

You'll need to JailBreak the device before restoring. Then you'll need to go through the same process you took to create the image, except the values of the if and of arguments will need to be swapped.

Additional Reading

I was searching for information on this myself because I needed to back up my email data from the device before doing a restore (it's just shameful that Apple doesn't consider your email messages to be important enough to include in its backups). The following information is valid for IOS 6, I hope it applies to your situation with IOS 3 as well. On IOS 6 at least, you won't need to mess around with SQlite or anything, it's all plain text.

You need access to the filesystem on the device. There are various PC and Mac apps that will browse the files on the device -- Ifunbox is one that claims to allow access to the filesystem without jailbreaking.

Instructions for jailbreaking your specific device (if it turns out you need it) can be found at http://stateofjailbreak.com/guide/iphone-3gs/3-1-2/.

The emails are stored in User/Library/Mail (that's a symlink, the actual path seems to be var/mobile/library/mail). Just copy the whole thing to your laptop.

Inside there, you'll find directories named after each email account set up on the device. There's a pretty self-explanatory folder structure within each account folder. Once you drill down, the emails themselves are stored in individual plaintext *.emlx files, complete with all headers and uuencoded attachments (there's also sometimes an "attachments" folder which has the extracted version of the attachments). On a PC, you'll want to rename them to *.eml files, and then you'll be able to import them into various email programs like Thunderbird or Outlook; with some you'll need a utility, with others the import function is built in.

I haven't gotten far enough to determine if copying a backup of these folders onto a device restored from itunes backup will restore your archive of emails or not. Did I mention how annoying it is that Apple doesn't think your offline emails are worth saving when you do a backup of your device?