Cannot file HTML email received on POP account in IMAP folders

Question

I've got a 2 year old MacBook Pro and use MacMail for email here at my job.
I've had the same set up for 2 years now, with 2 pop3 accounts set up just on the MacBook, and my main email set up also, as an IMAP, with folders underneath, that is also on my phone and iPad.
One of the 2 pop3 accounts receive emails on things like phone bills, internet bills, etc....
The other one receives efaxes.
When emails come in to my consolidated inbox, I work that inbox like a "to do" list, and file or delete emails when the task is done.  
Ever since upgrading to Mavericks a month ago, I can no longer file HTML emails that come in to the pop3 accounts in to the folders on the IMAP account as I always have done before.  Most I delete, but things like receipts from Amazon must be kept (for business records). 
When I try, I get this message.  I've checked with our email host, and they've spent many days on this and do not feel it is a problem on their end.  Any thoughts?

Answer 1

I need to be able to move all my emails from one install of Mac OS to another, I reinstall a lot, because I always screw something up.
No, you don't need to reinstall a lot. The problem is rarely the application itself, so doing that is a huge waste of time and creates more problems. It's much easier to solve the problem at hand rather than reinstalling things.
The problem is that when I do this, and set up an email account again, messages are redownloaded, regardless of how I organized them.
Then you should move your entire Mail folder out of ~/Library, onto your Desktop, and once you have your emails downloaded again and everything else works, delete that folder on the Desktop.
Is there any way to get Mail to remember which message it last downloaded after I set up a new account and add in my custom mailboxes, so no duplicates are made?
No. Refer to the solution just above.
Every once in a while, I go on Live Mail, and move all the messages in inbox to a folder called Archive. Mail only downloads the Inbox folder, so my mail is safe on my mac and safe on the server. Is this a good solution?
Only as long as you have a full backup of your Mac at all times, and the Windows Live Hotmail service doesn't go south without warning.