What time did that old text message come in on my iPhone?
Have you noticed on old text messages the time is not always displayed?
You can see the exact time an old text message came in and what time you replied by:
Opening the Messages App
Tap on the message thread that holds the message you would like to review
Scroll back and find the message in that thread that you would like to review
Swipe from right to left on the screen and the detailed time will appear on the right