Hi Mark,
For the first question: Can anyone say whether this is a true statement, or is there a known way to migrate from another hosted Exchange provider other than with IMAP.
Answer: At present, if you have Exchange 2003 Server or later versions in on-premise, you can deploy cutover migration, staged migration and Hybrid to migrate users to Office 365. If you use Non-Exchange on-premises messaging system, you can use IMAP migration to migrate users.
For more information about migration type, please refer to the information in “Compare migration types” in the link below:
Mailbox Migration to Exchange Online:
http://technet.microsoft.com/en-US/library/jj863291(v=exchg.150).aspx#comparetypes
Additionally, The restrictions apply to IMAP migrations :
1.Only items in a user's inbox or other mail folders can be migrated. You can’t migrate contacts, calendar items, or tasks.
2.A maximum of 500,000 items can be migrated from a user’s mailbox.
3.The maximum message size that can be migrated is 35 MB.
For the second question: Use PST file to import\Export data.
Yes, use the PST file to import data to Office 365, we can import emails, contacts and calendars. However, you cannot import the PST file to Office 365 directly. You can let the users add the Office 365 account into Outlook client using autodiscover,import the PST file into Outlook. Then the data in Outlook will sync to cloud.
Furthermore, about how to deploy IMAP migration, please see the step-by-step information in the link below:
Migrate Email from an IMAP Server to Exchange Online Mailboxes:
http://technet.microsoft.com/en-US/library/jj874015(v=exchg.150).aspx
Thanks,
Linda Wang