Move from Intermedia hosted exchange to MS 365 hosted exchange

We moved from in house exchange to hosted exchange with Intermedia 3 years ago.  It was pretty straight forward.  I was able to sync my mailbox store with theirs and let it sync for a week before changing my mx record.  I can't seem to find any info on moving from a hosted to hosted solution.  Anyone else done this?  We have 250 boxes, Intermedia is currently on exchange 2010 and MS 365 will be exchange 2013.
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For me just imagine intermedia is your hosted exchange. To move from your hosted exchange to Office365, you have to contact purchase the packages from Microsoft, setup AD synchronize with Microsoft and etc.

So, it is intermedia who will doing this job. The question are they willing to do that?

Since you have few mailboxes, the quickest way is ask your user to export their mailbox (email, contact, task, calendar and etc) to PST format. Then subscribe Office 365, push the PST to new mailbox on Office 365 and terminate with intermedia

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