Hi Charles,
You may follow this informative guide that describes the steps to accomplish this task in quick way : searchexchange.techtarget.com/.../Quick-tricks-for-migrating-Exchange-UM-to-Office-365
Moreover, to migrate users mailboxes from exchange 2007 to Office 365, you may also consider on LepideMigrator for exchange(www.lepide.com/exchangemigrator ) that could be a good alternate solution for you.