Migrating from Exchange 2003 to Office365...multiple domains in 2003 Exchange, best way to move just one?

An Exchange 2003 Server hosts email for multiple email domains. We are moving one of the domains to Office365.  I will call it @a.com. There is a tool in the Exchange Admin Center for batch migration, but it looks like it will grab all domains we have on our server. I don't see a way to move only @a.com while leaving @b.com. I know it is an option to export all mail items for each user to an Outlook pst and import them into the new mailboxes, but I am hoping there is a better way.
@a.com is the only email domain on the server that uses public folders. Is there a best way to migrate all of those? I understand migrating those by way of a pst may take a long time for all the items to show up in Office365, so is it better to move them to subfolders of a shared mailbox?
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If not mistaken in EAC, you have an option to use batch migration with CSV file.


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