Yes, you can use e-mail "forwarders" that can be set up to send a copy of the messages from
b@domain.com to
a@domain.com as well as the intended recipient.
If you are Linux based, log into cPanel and select the "Forwarders" option in the e-mail category. That will guide you through setting it up.
Don't hesistate to ask me if you need any more help

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