To be fair, this was difficult under IBM as well, once we moved into the Verse cloud.
Your Current Procedures aren't WorkingWhen I first started trying to get backups of files, I had a lot of people tell me how easy it was. I followed their advice -- and yes, it was easy. After all, there's a menu option inside outlook that lets you export directly to a PST file.
It was too easy. I was suspicious though. Suspicious that a person with a 10 year occupation could have a mail file that was a mere 400 MB. I looked into it and sure enough, the outlook method only gives you a recent subset of your data.
If you've been backing up PSTs from the cloud using outlook, you're missing a lot of data.
Does the Problem Need Solving?Before I go into the details of how to solve this problem, it's worth mentioning that there is another workaround that might be more suitable. I'm talking about Shared Mailboxes.
In Office 365, you can convert a user's mailbox to a shared mailbox and allow other people to access it. The downside of this is that you no longer have a perfect legal representation of that mailbox as it was when the user left (as new users could potentially edit, delete and add to it). The good news is that shared mailboxes don't consume office licences though unfortunately, you can't delete the original users from your active directory. They're still required to be present for the mailbox.
In our case, we keep a copy of all mail files in PST format for our records - and we use shared mailboxes only when necessary to provide access when someone critical has left. Shared mailboxes of previous employees should generally be a fairly temporary thing.
How to Archive to PSTThe PST archiving process is a little convoluted but it's accurate as it gets the mail file information from eDiscovery. Once you have your PST, and you've tested it of course, you can delete the user (or convert the mailbox to a shared mailbox).
So, without further ado, here's the instructions via slideshare.