You can use FileMaker with the ESS feature
See
Accessing External SQL Data Sources (ESS) Overview and Troubleshooting
Or if you like to use MBS FileMaker Plugin, check the SQL functions.
They allow you to connect via script, run some SQL commands and move data.
Either record by record yourself in a loop or with powerful batch functions like FM.SQL.InsertRecordsToSQL or SQL.InsertRecords and similar ones.