Email migration

In our CRM program there are a few thousand contacts, and each one displays all of the emails we have exchanged with that person. Soon we need to update the email address that we use with this CRM. However any time the email account is disconnected from the CRM all emails are removed, which means that we would have to waste a lot of time manually looking in Outlook for the email history of each customer. We need to find a way to copy the emails from the old inbox to the new inbox in such a way that the CRM will recognize them and match them to the correct contacts.