There are two ways you can save the contents of the former employee's mailbox:
1. Add the former employee's email address to your version of Outlook 2013 or 2016, and then export the data to a .pst file to save the contents. You can import the data to another email account as needed. To learn how to do this, see Get access to and back up a former user's data.
OR, if you have an Enterprise license (E1, E3, E5)
2. Place a Litigation Hold or In-Place Hold on the mailbox before the deleting the user account. This is much more complicated than the first option but worth doing if: your Enterprise plan includes archiving and legal hold, litigation is a possibility, and you have a technically strong IT department.
Once you convert the mailbox to an “inactive mailbox,” administrators, compliance officers, or records managers can use In-Place eDiscovery tools in Exchange Online to access and search the contents.
Inactive mailboxes can't receive email and aren't displayed in your organization's shared address book or other lists.
To learn how to place a hold on a mailbox, see the TechNet article Manage inactive mailboxes in Exchange Online.
For more information on how to secure a former employee's Office 365 data see Overview : Remove an Employee and Secure Data in Office 365