Here are the steps to transfer your backup from one device to another:
Make a backup
iOS/Android: tap on Settings/Backup (or in the old versions, More/Backup)
Mac OS: File > Backup
Windows: File > Backup
Save
Save the backup file to your cloud storage (Dropbox, Box, Apple (iCloud) Files, Google Drive, OneDrive ...)
or email it to yourself.
Recommended: keep it as an archive so your songs are safe;
Recommended: occasionally do backups in iReal Pro in case of hardware failure, resetting, loss, damage etc.)
Apple users can simply use Airdrop to transfer songs, playlists and backups between their Apple (iOS and Mac) devices. Also iCloud sync will automatically sync songs, playlists if enabled in iReal Pro Settings.
Import
(Very old versions before iReal Pro 5.0.4 cannot import backup files)
iOS: In Dropbox tap on the BACKUP.html file, on the top right, tap on Share, Export, Open in and select Import with iReal Pro. In Mail, tap and hold the BACKUP.html file and choose Copy to iReal Pro.
OS X: drag and drop the BACKUP.html file over the iReal Pro app icon in the dock of your computer.
Android: From the cloud, open the BACKUP.html file with iReal Pro. Import from Dropbox or Drive information here.
From Email, touch the Backup file name itself to import,
or touch the Download icon to Save to internal memory, or touch the Drive icon to save to your Drive cloud storage, where you can subsequently tap and choose Open with from the 3 dots overflow menu.
Windows: File > Import
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Example: from Android to Windows, set up Drive in each, save backup file to Drive, then in Windows, File > Import ... from Drive.