This was the question posed to me by Monique M. Ferraro, the principal of Technology Forensics in response to my last post. It is certainly true, as she pointed out, that law enforcement has a pretty easy time of getting data - it's much tougher in civil cases.
Generally speaking, if you are involved in a lawsuit, you can subpoena records that might give you dates and times of calls, the phone numbers involved, call duration, customer information, etc. However, if you want content (texts or e-mails) you are up against two things - first, most carriers don't hold the content at all - or for very long. Second, they will (appropriately) decline to hand over any content citing The Stored Communications Act.
Thus far, all the court cases have upheld the principle that the SCA prohibits divulging stored content. However, you may find what you're looking for on the opposing party's phone - or, if they sync to a computer, on the computer in the backup files. Where content is involved, you'll need to go the user - exactly as you must do when you want the content of social media sites.
By the way, I neglected to say in my last post, which described how long carriers store your personal cell phone data, that the information sheet I reference was dated 2010. An investigator specializing in this area confirmed to reporters that the sheet was still basically correct.
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