Remark: The guide below uses AST Android SMS transfer for Windows version screenshots. The way to finish your task on Mac is almost the same.
After importing the .db files to the AST Android SMS transfer, the backup SMS will present automatically.
There are two modes, view mode and edit mode. In both modes, you can print, delete and export the SMS.
In the edit mode, you can edit a certain SMS by double click the message.
Note: Exporting is a great feature for you to save the backup SMS in csv, txt format permanently.