Hiding or archiving texts messages on an iPhone without deleting them

One great feature of the 'Messages' app on an Android was that you can quickly 'archive' a text message and remove it from the list of text messages on your screen. When you sent a new text message to the same recipient, the entire 'archived' or hidden text string was pulled up. This was a great help to me keep on top of my text messages and clear the clutter. Is there a way to hide or 'archive' text strings on an iPhone that keeps the message string easily accessible and pulls it back up when I text that person again?