macOS Messages – How to Copy Entire Chat in Mojave

Go into the conversation on your iOS device (assuming iOS10). In the top right corner you should see an information symbol ("i" in a circle). Click on it. Then scroll down to the picture you want to delete. Then tap and hold the picture. Three options will come up: copy, delete, more. Select delete. If you're using an iPhone 6s or newer, be careful not to force touch the image instead of tapping and holding.

Per @Tetsujin's comment, I started down the path of what was linked. It didn't work, though. After transferring in the folders/files, Messages looked the same as before.

It got me looking for a similar answer, however, and I was able to come across this article on iMore.

The basic gist of the article is to copy the contents of ~/Library/Messages from the Old Mac into the same directory on the New Mac.

[Insert standard "back up your stuff before doing this!" comment.]

Then, I did a reboot (which I hadn't done with the prior attempt; maybe that was the difference).

Note:

The iMore article seems to indicate that the "Archive" folder is only for conversations that have been closed, and only if you have the "Save history when conversations are closed" option checked. I did not have this option checked, and I rarely close conversations, and all of my conversations were there.

Note 2:

The folders from the original answer in Tetsujin's comment were aliases, and I don't know if they are pointing to the folders in ~/Library/Messages, but – for whatever reason – iMore's solution worked! (Perhaps it was the recommended reboot found in iMore's article.)