Configuring hybrid deployment and moving mailboxes will work as expected, but Microsoft suggests keep one Exchange server for user management.
How to decommission your on-premises Exchange servers - How to Remove Failed Exchange Server from Active Directory?
Step by step guide for Migrating 2007/2010 to Office 365 your reference: Migrating Mailboxes from MS Exchange 2010 to Office 365
And If you want to go with a third-party tool, you can check EDB to PST Converter tool.
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