Can I obtain copies of my text messages

No. The only way to see text messages is on the phone. It would take a court order to be able to see text messages any other way.

There are many softwares you can install on the phone to capture these once you have installed this software you can set parental controls on it and have it text or email copies to you from the other phone. But, you do need access to the phone to initially install the "spy" or "parental control" software. FBI suggested a software to me, can't remember name, but can find if this helps you, something like "phone police" not sure off hand. It works over internet so you need data or continual wifi on the target phone. Didn't work for me, I don't give the kids data usage, and limit their wifi most of the time.

Gophone users no you cannot obtain copies of your messages and what they say.  But if you are on a contract phone all you do is make sure you use Google Chrome web browser go to www.att.com/messages. And yes you can see every word in sent and recieved text messages.

                                                                                                       kimmy_d

GEt an App for phone and it will auto copy all text an phone calls  to your Gmail acount you can set it ever 30 to day or week.

How long does AT&T store text message content for court order purposes?

I have the att messages set up, however, it's only showing my phone.  How do I look at the texts on another phone on my account?

Each phone on the account has to sign in for its own messaging account and the first time is authorized on the phone.  

After then you can sign in on another device and a code is sent to the original phone.

I use AT&T Messages on my PC.  Even though I delete my messages from my iPhone, they are still maintained online.  I like that because I know I can always go back and look at them if I need them.