You enable Messages in iCloud both on the phone in the iCloud preferences and in the Messages app preferences on the Mac.
Once the messages are uploaded to the iCloud server, they are all available on the Mac’s Messages app, where they can be copied out one conversation at a time. Photos can also be saved.
I wish it were as easy (and free) on Windows PCs, but I couldn’t find a free way to sync conversations from the iPhone.
If you search online, there are dozens of apps that tell you that they’ll copy or move or backup your iPhone data to a PC without using iTunes.
I couldn’t try them all, but in reading some trusted sites, I did find a utility called iExplorer ($39.99) that does a good job of moving data from iPhones to Windows PCs or Macs.
With iExplorer, you connect your iPhone to the computer with a USB cable and you’ll be able to move and back up all kinds of data, including messages, music, photos and other files.
iExplorer has the added benefit of being able to read data from your iPhone’s backup in iTunes.
The good thing about iExplorer is that you can download the app and try it for free in demo mode, which will let you see the messages from your iPhone. You won’t be able to export them until you pay for the full version.
Android users can use the free app SMS Backup+, available on the Google Play App store.
Jim Rossman writes for The Dallas Morning News. He may be reached at email@example.com.