Instead if copying and pasting text messages you can forward even entire conversations directly from your iPhone.
Begin with the message you are interested in. Hold your finger on it for a second (or double-tap it). An icon with "Copy" and "More" should pop-up. Tap "More". Then you can select which part are about to be forwarded. Once you've selected everything, tap the arrow in the lower-right corner. Selekt to whom you want to send the message and tap "Send".
