If you’ve migrated your e-mail to G-Mail using Google Apps Sync…. You may notice that Folders do not show up on your iPhone/iPad. If you log into the web interface, you can rename the labels (e.g.) Inbox/Sub Folder to INBOX/Sub Folder and it will show up on the iPhone. This is because of some funkiness that happens between Outlook and G-Mail and IMAP. Your best bet to fix this problem is to move the folders out from under the Inbox. You can move them to the same level as the Inbox or into another folder which is itself at the same level as the Inbox. You can do this from either the Label section of G-Mail webmail (just remove the Inbox/ or INBOX/ portion of the label), or from Outlook.