I am currently migrating my >4GiB of mail data from GMX to MobileMe. I have been using offlineimap regularly to backup my mail data. So first step was to update the backup. Now the next step is to run imapsync, which can migrate whole IMAP accounts. The full command I am using for this is:
imapsync --sep1 '/' --prefix1 '' --ssl1 --ssl2 --authmech1 PLAIN --authmech2 PLAIN --host1 imap.gmx.net --user1 "firstname.lastname@example.org" --host2 mail.me.com --user2 "email@example.com"
I will report back once the sync has finished, this might take a while.
Update: Yup, it worked. My mail is now hosted on MobileMe. More disk space. What is missing at MobileMe is that it does not support automatically expiring mail folders. I.e. for mailing lists, I sort the mails into subfolders for each list. The lists are often high volume traffic, and not very important. So I'd like the mails to expire after, say, 30 days. With GMX this was not a problem, but MobileMe does not yet have such a feature. However, I found a nice tool called imapfilter. It allows you to do all kinds of stuff, besides other things it allows you to filter mails according to date and to delete them. This is what I will do. I'll write another post, when I found out how to do that exactly.