Syncing downloaded itunes

Device backups and library backups are different things. In particular device backups don't include media, which has certainly caught people out before now.

• See Backup your iTunes for Windows library with SyncToy - Apple Community for a way to both backup your iTunes library and then update that backup efficiently by copying only new and changed files.
• See Move your iTunes library to a new computer - Apple Community for advice on transferring the library from one computer to another.
• When moving a device to a new machine it is normally sufficient to create a fresh backup there and ignore those on the old machine. See Archive iPhone backup in Windows - Apple Community if you really want to try to copy over and access the old backup set.
• See Sync your iPhone, iPad, or iPod using your computer - Apple Support for steps on copying your library to your device. You can either sync over USB, or take out an Apple Music subscription so that syncing takes place via the cloud. Note Apple Music is a library syncing service, not a backup. You should always retain original copies of your music files.

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See Sync your iPhone, iPad, or iPod using your computer - Apple Support.

If there is content on your old device that isn't in your computer or backup then see Recover your iTunes library from your iPod or iOS device - Apple Community.

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In general you cannot transfer media content directly from device to device. It can be recovered into a library on a computer, and from there copied to a new device in the usual way. With an iPod touch you could potentially subscribe to Apple Music which could upload the music on the device to the cloud, from there it could be downloaded to a computer and your iPhone. If you go that route be sure to merge the content of the iPod with the cloud. If you chose replace in error all your content on the device gets lost. Manual recovery using iFunBox and Windows Explorer is an alternative route if you don't want to pay, however temporarily, for Apple Music.

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