Carl's sources hold the view that the treasures were put in the Nea Church (on which more, recently, here). Well, it does have a lot of vaults. But unless there is new information that I don't know about, placing them there is speculation.
Some years ago, Sean Kingsley wrote a book about the fate of the Temple treasures, God's Gold. Kingsley too follows Procopius and has the treasures returned to Jerusalem by Justinian, but he infers (guesses) that they were kept in the Church of the Holy Sepulcher (Holy Sepulchre). I blogged on the book (and yes, I did finish it) here and links.
Past posts in Carl's series on the Temple treasures are here and links. One more to go.
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