This application can't be used to transfer the music to your new phone, but there is a way. Install iTunes and create a backup of the music database using the backup operation available when you click the device name in iTunes.
File transfer won't be possible because of the created lists. Install iTunes and connect the phone, backup, then connect the new phone and use restore. Choose the previously created backup and restore it. The files and the playlists will be transferred to the new phone.