I've got a problem. Maybe the problem had been discussed before.
I once come across the problem that my iPhone rejects receiving new SMS but all the SMS are so important that I don't want to delete them. So I simply need to backup your iPhone SMS onto computer or print them or transfer to another iPhone?
Here I am looking for a way on how to transfer your SMS from iPhone to computer and keep them in safe.
Hope to get answers as soon as possible.

If the phone is jailbroken, you can use iFunBox/DiskAid/iPhoneBrowser to connect to the phone and download the actual sqlite database that holds the SMS messages (SMS.db, if I recall correctly). From there, you can use any of a number of free tools on Windows or Mac to browse the contents of the SQlite database, export to CSV or text, etc. It shouldn't require any pay software to do, so if you find yourself on a site asking for $19.95, skip it and keep looking.

Here is the simple to follow steps to Restore SMS History from Previous iPhone to New iPhone. All you have to do is to copy SMS backup files from old iPhone back up folder to new iPhone back up folder.

Navigate to the iTunes backup folder
1.Windows User : C >> Users >> User Name >> AppData >> Roaming >> Apple >> Computer >> MobileSync >> Backup >>
2.Mac OS X User : ~/Libary » Applications Support » MobileSync » Backup.

In the backup folder there will be X number of folders according to number of phones you synced to your iTunes. For example i have two iPhone 2G and 3G so i have two folders named with 40 random hex characters. But i need to copy SMS from iPhone 3G so how do i identify?
To identify your particular iPhone backup sync both phones with 5 minutes of interval and note the time in your computer clock while syncing.
Now Sort the view by date–this will let you easily tell which subfolder belongs to which phone.
Now you knows the folder where your previous iPhone 3G backup is saved, so explore to that particular folder (iPhone 3G) and copy these two files to iPhone 3GS folder. Make sure you must synced new iPhone 3GS at least once so back up folder will be created.
3d0d7e5fb2ce288813306e4d4636395e047a3d28.mddata
3d0d7e5fb2ce288813306e4d4636395e047a3d28.mdinfo

Closing thread, it just attracts spam for pay software when this can be completed free and easily and it is already detailed in the thread.