Hi,

My question is, can an expired Active Directory user to receive emails in your Exchange mailbox.

Regards,

What do you mean by "your mailbox". If you mean that you want to redirect emails from expired user to your mailbox, then yes, you can do it by using transport rules on Exchange server.

Expired AD account is equal to the manually disabled AD account, so if the mailbox type is user mailbox and when account expires, that mailbox wont be able to send\receive emails

In order to send/receive mail, a user must log in to AD. Expired user accounts cannot log in.