You can review text messages from an Apple iPad or iPhone using Decipher TextMessage. A trial version of this software is available here. I tested the software on my iPhone this evening, and it easily allowed me to access text messages from as long as 8 years ago. Not an easy task to accomplish on the phone itself. As you can see below, messages are sorted by the numbers or individuals (or groups of individuals) you exchanged texts with. [I'm not showing the names of my friends, but the list in the middle will show names, not just numbers, when the recipients are known.]
Simply selecting ''Copy All Conversations on Device" from the drop down on the Copy icon on the toolbar will quickly copy all message content and associated metadata to your clipboard. It looks like this pasted into an Excel spreadsheet, and you can see that it can be parsed out fairly easily.
Better yet you have the option to export text messages with their attachments.
Decipher will create folders with named with the sender's name and number, and include subfolder containing all attachments.
Decipher gives you the option to recover deleted messages and fragments of deleted messages. Running the recover tool will export these to a html page. iPhone backups contain a Message app database from which deleted messages are recovered.
Decipher will also automatically search back-ups of your iPhone and recover old text messages. A license for the software only costs $30. Note that Craig Ball refers to Decipher a tool to preserve text messages in his e-Discovery workbook. See the Tip of the Night for April 1, 2017.