The best way for now, until we have sync'ing available, is to use the 'Backup/Restore' from the left menu. Have a look at the instruction manual here
https://www.blueletterbible.org/android/man01_1.cfm.
Once you create a backup, it will be in the device's Download\BLB_Backups\ folder. You will need to transfer this backup file to the new device into the same location. You may need to create the BLB_Backups folder. This may be easiest by having the new device perform a backup. This way it will create the folder for you.
Once the file is in place, start up the app, and tap the backup file to perform the restore.
Let me know if you need further assistance.
-=Dan