You can easily  migrate Office 365 mailbox using EdbMails Office 365 Migration tool which allows you to migrate mailboxes form Office 365 to Office 365 / Live Exchange Server. It also supports Office 365 to Hosted  Exchange server Migration. Even you can export Office 365 mailbox to PST.  It will migrate all the  mailbox data such as Emails, Calendars, Contact, Tasks, Public folder, Shared Mailboxes, Mailbox and folder permissions, etc without any data loss.

You can easily handle the tool with its easy to use GUI and  simple procedures.

Office 365 Migrate Mailbox

High performance Office 365 Migration
Migration of Office 365 Mailbox of any size
It will  automatically set  impersonation rights to source as well target server.
Automatic  creation of  mailboxes on the target server
Automatic mapping of  source and target mailboxes
Automatic migration of  mailbox and folder permissions
Easy handling of Office 365 throttling during migration
High-speed Office 365 migration with automatically managed multi-threading capability