Why would you want to download text messages from your iPhone?
Family court cases depend a lot on the particular facts of that case, and it probably won't surprise you when I say that parties often don't agree on the facts. This means a judge can get two wildly different versions of the "facts", and then the judge is left to assess teh credibility of the witnesses to decide who is telling the truth. Because communication by text message is so ubiquitous these days, text messages can be a great tool to support your version of the facts. If you can produce text messages from the other party that support your version of events, or that contradict the other party's version of events, it can greatly improve your credibility with a judge.
Why shouldn't you just screenshot your text messages?
This question should probably be restated as "What makes a good exhibit in court?" When you screenshot a text message, it generates a picture, usually a .jpeg file. If you are sending these to your attorney, for example, your attorney is left to sort through dozens, or hundreds, or even thousands of pictures. This is a real pain in the @$$. Your attorney or his staff will probably end up converting all of those text messages to individual .pdf files, and then joining those files into one .pdf file. You will also be charged for the (often significant) amount of time spent doing this. Even the resulting .pdf is not ideal because each page will just be a single screenshot, it can be difficult to see who is saying what, and the flow of the messages is all broken up. This is a situation similar to sending separate pictures of each individual page of a document, rather than just sending the document as a single .pdf.
How to download text messages from your iPhone
While investigating different ways to get text messages off of an iPhone and into a usable .pdf format, I came across “Decipher TextMessage”. I tried the free version and it seems pretty straight forward. The free version will not let you download all of the messages – they of course want you to buy the paid version which is $30, which is probably well worth the money. This application will let you search for particular words in your messages, and will let you download particular date ranges. You can then output your text messages into a searchable .pdf document that is easy to use, and easy for a judge to read.
Why should you pay for such an application?
There are a bunch of free applications that claim to do the same things, but most of them seemed very spammy and involved a high likliehood that you would also be downloading some malicious software that you don't want. Decipher TestMessage appears to be legit, and won’t destroy your computer with malware (I didn't get any). I think $30 is a small price to pay to avoid malware or some infection on my computer.
Where to go to get started
This page has directions on how to get your text messages using Decipher TestMessage. You will need to backup your iPhone using itunes first. The only problem I ran into was doing the backup – the first backup was encrypted, and I had no idea what the password for that was. I unchecked the “Encrypt iPhone backup” box and made another backup, and from there it went smoothly. Once I selected the contact and related text messages, I could print to .pdf. I should also note, I did this in windows and not on a mac, but this software is available for both Mac and Windows.