In order to migrate AheadWorks Blog for Magento 1 to Magento 2 Blog please install free Magefan Blog Extention.
Thereafter, please go to Admin Panel > Content > Blog > Import.
Choose the "Import from AheadWorks".
Blog Import from AheadWorks
Specify M1 database credentials:
1. Set a Database Name and User Name.
2. Set a database user Password.
3. Set a Database server host (location of a database) in Database Host field.
4. Set an Table Prefix if there is one.
5. Specify a Store view the blog from AheadWorks is to be imported to.
Once you have finished don't forget to press a Start Import button.
Troubleshooting
1. Something went wrong: Warning: mysqli_connect(): (HY000/1045): Access denied for user
If you have received this error, try to copy AheadWorks blog tablets from Magento 1 database to some database on the same server as Magento 2. As far as you have done this, try to specify new database credentials redo the blog import from AheadWorks.