...you merely install iTunes in the new computer, login to your account and everything updates automatically. Correct me if I am wrong.
I downloaded iTunes to my new computer but my iPhone will not back up - I need to transfer the iTunes library from my old computer to my new computer. I followed the iTunes instructions but it refers to "iTunes purchases". I need to transfer all music in the old computer iTunes library to the new computer. I tried to transfer via a flash drive but it transferred in some strange computer language. How can I transfer the iTunes library to the new computer? I don't really need the library on the old computer any more. I did deauthorize the old computer but that did not help.
I need to update my phone and can't because it asks me to back up my music and I can not do that - thus I can not update my phone.

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