Did you deploy a hybrid environemnt with the on-premise Exchange server? Whether the user is assigned an o365 license?
What migration method are you going to use?
The easiest way is to let the user export the on-premise mails through outlook then import them to the mailbox in cloud, change the MX record to make new mails coming to cloud.
You may also refer to the related thread here discussed the similar issue, in a hybrid environmen if you have assigned a license to the user which lead the user has an o365 maibox already : Exchange 365 Migration - Single user, dual mailboxes
Backing up the users 365 mailbox to PST
Revoking the 365 license (which deletes the 365 mailbox)
Forcing an Azure AD sync
Migrating the on-site mailbox to Exchange 365
Re-assigning the license
Importing mails from the PST back into the 365 mailbox again
For more information about How to merge an Office 365 account with an on-premises AD account after hybrid configuration?
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