You can forward all e-mail from the old admin to the new one but there should be a point in time when this no longer occurs — particularly, if messages will be forwarded to the new mailbox and kept in the original mailbox. The reason is the likelihood is that the old mailbox will go unmanaged and messages will continue to accumulate and consume disk space. There is also the risk that personal e-mail messages will be forwarded, which may present some liability concerns. These are some options for new messages only.
It is possible to grant access to the old assistant’s mailbox to the new assistant by setting the appropriate permissions in Active Directory. Refer to the following TechNet article: Understanding Exchange Server 2003 Mailbox Access Delegation for details.