Due to Verizon's choice of protocols (POP), the only folder that will download to your email client is the inbox. The Sent folder will not download, nor will any custom created folders, Trash, etc.
If you are very determined to have your sent messages, you could try logging into webmail and moving all of the messages fromt he Sent folder to the Inbox to be downloaded, then move them to the Sent folder once they are downloaded in Outlook.
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