Last time I did a mail migration, I installed BincIMAP, which is about as simple an IMAP server as can be, and configured access to this local IMAP account in both mail clients.
I copied all mail from the “Local folders” account to the IMAP one, and it is still there. IMAP is very handy: all your mail available in any IMAP-aware client; you can change your email client twice a day if you want!
BincIMAP makes your email available through IMAP and stores it in a Maildir/ directory in your home folder, in Maildir format. Many advantages:
— The mail is in the home folder, so any backup of your personal data also includes your mail.
— IMAP: see my comment above about choice.
— Maildir storage: you can thus use text-mode clients that read the Maildir format when you connect remotely, or use new-mail-notifiers that know of Maildir, but don't handle IMAP.