The Cross-tenant mailbox migration function in new Exchange online admin center will migrate mailbox from one tenant to another tenant rather than only emails. After migration, mailbox will hosted on new tenant.
If you want to migrate mailbox to hosted on another tenant, you can use this function, before migration, you need to do those prerequisites.
If you just want to copy emails from one mailboxes to another mailbox, you may need to export/import email from Outlook client.
For more detail information about Cross-tenant mailbox migration function, you can have a look about this article: Cross-tenant mailbox migration (preview) (There also exist some limitation and know issue with this new function, you can see from the end of this article)
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