The ringtones show up in iTunes, but iTunes says that it cannot find the songs in order to restore them to my iPhone.
How do I get these ringtones back without having to go and redo it again?
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Play the tones in iTunes to make sure they have not been corrupted or moved.
It's most likely that the iTunes library expected the tunes to be stored in a certain directory on the disk and now the file is missing or moved. If there are things moving, you'll have to decide if you need to run a disk repair tool on windows or if someone may have moved folders or files or some other hardware issue is at hand.
It's likely this happened some time ago since if your phone had all the ringtones for months - iTunes wouldn't need to send them, but the restore made it need to actually send the file and now it's missing.