Another method for preserving emails that scales more effectively than the shared mailbox hack is to use a retention policy (sometimes called litigation hold). Enabling mailbox retention prevents the mail from being deleted even if the mailbox itself is no longer available.
It is important to keep in mind that to use mailbox retention as a strategy, the administrator must have at least an E3 license, though our tests have shown that it can be enabled for users who have lower end accounts such as Business Premium. (You must also be in the legal hold, or more typically a discovery management, administrative role.) Thus, if you're connecting through a Microsoft partner account supporting the end customer, ...