Q: My iPhone 5s Messages and MacBookPro message conversations used to sync on both devices.  Now a message on one does not appear on the other.  How do I fix that?

I discovered that I had turned off "Text Forwarding" to my MacBook in the Settings/Messages menu of my iPhone.  I'm not sure why (ignorance?) I had done that, but I really think the function is mis-named.  Perhaps "Text Synchronization" would be a better title?  Also, the actual synching process is not intuitive or described very well.  It consist of sitting at the device you wish to forward (synch) text with and having your iPhone with you as well.  Via the Settings/Message menu, select "Text forwarding." There will appear slide switches for other devices on your network.  When you slide the switch to the right (on) for the device you are setting at, it will start Messages if not already on, a window will open and display a 6 or 7-digit (I forgot) number which you key into the window that has appeared on your iPhone and press "Allow." Now messages sent or received on either device show up on both.  Thanks for your answer.  I didn't know enough at the time to ask a good question.