How do I synch emails that are in the iCloud Mail on my phone to where I can see them in the icloud.com/mail in a web browser?

I have a private domain and I moved the emails from that IMAP account on my phone to the iCloud Mail account on my phone. But if I go to icloud.com/mail, I don't see the emails there.

Is there a way to force a synch from iCloud Mail on the phone so the emails are available via a web browser?