From Decipher Media:
Save your iPhone SMS text messages to your computer with Decipher TextMessage. Never lose important conversations again. Quickly load messages from your iTunes backup. Save and view image and video MMS attachments. Easily see conversations by names in your Phone's Address Book. Recover deleted iPhone text messages. Supported for Windows 2000 and above. Export conversations in text and HTML formats.
What's new in this version:
Updates to be compatible with iOS 10.
New preference setting to include name and phone number on every text message. This can be useful to ensure text message transcripts are admissible in court.
Easy to use interface with intact saving of iMessage contents in convenient format. My version was not intended for recovery of deleted MMS, but handles archiving of conversations very well. I always balk at paid applications, but this gets the job done well. Customer service team is responsive and helpful.
none i can think of
Updated on Jan 9, 2014
Just remembered that it, in fact, DOES save the deleted files. I was recalling another program.
The cheapest solution I've found. Some other programs were $60 an $100! I really wanted to retrieve my text messages but couldn't justify that much money. This was only $20. It installed with no problem and extracted all my messages.
So far I can't see how to choose the backup from which I want to extract my texts. It isn't immediately obvious but I haven't investigated it fully so no real criticism.
I accidentally deleted all my text messages from my husband - four years worth! This isn't the first time I've done this. So I wanted something to extract the texts so i could save them as a text file elsewhere (since I clearly can't be trusted with saving them on my phone :-).