matching email folders

Best way is to use an IMAP mail server (most providers offer an IMAP option), and store the folders on the server instead of "On My Mac". When you create a folder (mailbox) in Apple Mail (on the Mac), you'll be prompted as to where you want to store it. Change the location from "On My Mac" to the name of your IMAP account, and it will be stored on the server and available to your iOS Mail which also accesses the IMAP server.

Check with your specific provider as to whether/how you can use IMAP. You may have to remove a POP account and re-add it as IMAP. If you do this, be sure to store your inbox/sent mail in local folders first, as such messages may be deleted permanently when you remove the POP account from Mail.

Matt

If you're filing them to local folders, then they won't sync. Local folders are stored on the device. iCloud and IMAP accounts won't sync local folders. To my knowledge, iTunes sync local folders either.

If you need access on different devices to emails you file, then you need to leave them in the main mailboxes. Other mail applications like Outlook might let you create subfolders under the main mailbox.

I haven't tried this, but another option is to try to create mailboxes under the IMAP folder if you're using IMAP. The messages would be stored on the server. If you can get those mailboxes to show on the other devices, then it should work.