To migrate you Parse database, you might want to read the link bellow on Step 1 of the article: Migrating an Existing Parse App.
To start your migration, go to App Settings -> General, where you will find the subtitle Migrate to External Database.
Once you are there, insert the database URI that we will provide to you.
Parse will start the Database migration and show you the Current Progress, like bellow:
Once you are on this step, you must test your app to ensure things went well.
Now you have your data in our database! You can see anytime in Core -> Migration what you have migrated.