Another item to think about is how much access you have to your hosted Exchange environment. Do you have administrative access to Exchange so that you may make sophisticated changes? I've seen some hosting companies provide their customers with just the ability to set up mailboxes, while others give them complete access. The transfer will also depend on whether you have administrative access to Exchange and if your hosting provider is prepared to work with your firm.
When I used to work for an MSP, Shoviv was my go-to tool for migrations. The program performed an excellent job importing mail directly into 365 from any mail client. There is a direct Exchange pull option, however, Shoviv access requires specific Exchange settings to be changed. IMAP migrations are a constant option as well.
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