Migrating database from old software to new software
Create a second MySQL database. This will be used for the migration and then dropped. These are known as staging databases. Make it an exact, table-for-table copy of your source. This way it is easy to export form the source and import into staging without worrying about mapping columns. The documentation will tell you how to load flat files into tables, and what formats it supports.

Once staging is fully populated write however many INSERT .. SELECT statements you need to map staging columns to the new DB columns and copy the data.

Do all this in scripts, not through the UI. Then it will be reproducable, debugable and audited. If you find a problem in the new app you can fix the script and re-run.