You can back up all texts, Playlists, and Replace Words to the notes app, Gmail, or anywhere to restore it later.  You cannot back up other settings of Voicepaper.

Tap Data Backup on Settings.

Select an app like Notes to save data.

To restore it from an app like Notes, tap the backup file.

Tap action button.

Tap Save to Voicepaper to restore it.

Please note that your current Texts, Playlists, and Replace Words will be overwritten.