Outlook Mac 2011–Transfer sub folders from one imap account to another

I use Outlook 2011 as an email client. I have an IMAP account with several subfolders and I have a lot of email in these folders which is stored on the servers of my ISP.

I have recently signed up with BT, mainly to get BT Sport, but I want to use my BT mail address for future emails. I need access to the emails stored on my initial ISP's servers, and thought I could do this by setting up new folders on the BT server and copying the emails from the initial folders into them. This seemed to work, but now, a couple of days after the copying, the mails no longer show in the new folders. I thought that perhaps the copying was not meant to work and started looking at exporting and importing the emails in the various folders, but I cannot get this to work.

Can somebody tell me how this can be done?

For background, the initial ISP also provides me with webspace to a domain I own. I have no future need of it and want to give up the domain, but if I do this now I will lose access to my email in the folders. I would like to transfer everything as soon as possible and close the domain but in practice it will have to continue for some time as, like many people, my email address on the old server is registered with lots of companies whose products I use. I have details of many of them, but some come as a surprise, today's being my ongoing sub to the Automobile Association. I think I will have to run both mail accounts for say six months to catch all of them before I can close the original account but it would be a big step forward to get the mail from the initial iSP' servers to the BT servers.