There are several easy ways to copy your documents from the free Notes Writer app to the Pro version:
1) If you use iCloud, open your files directly from iCloud Drive in your Notes Writer Pro
2) You can use “Files” iOS app to copy folders and multiple files from the “NotesWriter” folder to the “Notes Writer Pro” folder (both of them are the iCloud Drive default app folders). You can use the "copy and paste” method directly in Files app. Once copied, open the Notes Writer Pro, go to the “On iCloud” location and you will have access to all the copied folders and files.
3) You can drag&drop your files using the iOS 11/12 drag&drop gestures to copy documents from the free app to the Pro one
4) If you have only a few documents, a quick way is to copy&paste the content of your documents from old version into new blank documents in the new app using the “Paste” option. (If you have images don’t use this option).
5) Move your documents using the “Send to app option” in the share menu. Open your free app, tap the “Select” button and select a document. Tap the share menu button on the top toolbar then “Send to App” option. Choose the new "Notes Writer Pro” icon to send your document to the app
6) You can also use the iTunes File Sharing: You can connect your iPad to your computer via iTunes and use the iTunes "File Sharing" feature to copy your documents from free version to your local hard disk then from there to the new Notes Writer Pro. There is an Apple page about the iTunes File Sharing and how it works: