Mail.app and sent folder synchronization?

When I sent an email from my Gmail account in Mail.app on my MacBook, it shows up in the Sent folder. When I send it from gmail.com on a public computer or from my iPhone or iPad, it shows up in the Gmail mailbox in Mail.app (which is its own mailbox and not part of the Inbox section of Mail.app).

This makes it difficult when I'm trying to find a recently sent email because I don't use any one machine more than the other. I divide my emailing time between all my devices and I love how simply it works. Is there a way to get all sent Gmail emails to show up in the Sent folder under the Mailboxes section in the top-left corner of the Mail.app window? Thanks for any help!