Hi @Kevin Wade ,
You could migrate your IMAP mailboxes to Microsoft 365 or Office 365. When you migrate the user's email by using IMAP migration, only the items in the users' inbox or other mail folders are migrated. Contacts, calendar items, and tasks can't be migrated with IMAP, but they can be by a user. In addition, you may need to have the appropriate permissions and the source system supports IMAP migration in order for you to use IMAP.
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.
For some users who already have a mailbox, refer to this approach:
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
You could refer to the similar case: Exchange 365 Migration - Single user, dual mailboxes
Unable to synchronize directories, see if this helps you: How to merge an Office 365 account with an on-premises AD account after hybrid configuration?
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