Are you using a SD card that you would be able to transfer to your new phone? If so, just follow these steps:
1. On your old phone, hit the 'Export Stories DB' button in the main menu.
2. Move the SD card to your new phone.
2b. If you are using a new SD card, please copy all the folders starting with 'fanfiction' to the new SD card. Also copy the stories.db file that should be in the root folder.
3. Hit the 'Import Stories DB' button in the main menu of the app.
Please let me know if you run into any issues.
You can email me at firstname.lastname@example.org