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Converting to shared will preserve the mailbox content, so there should be no need for backup. As for the number of items mismatch, it might be due to some hidden items, filter configured during the export process, deduplication settings, incomplete .ost file, etc. <br />
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If the intention is to keep this mailbox to meet legal requirements, just use the Inactive mailboxes functionality: <a href="http://technet.microsoft.com/en-us/library/dn144876(v=exchg.150).aspx" rel="ugc">http://technet.microsoft.com/en-us/library/dn144876(v=exchg.150).aspx</a>
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Converting to shared will preserve the mailbox content, so there should be no need for backup. As for the number of items mismatch, it might be due to some hidden items, filter configured during the export process, deduplication settings, incomplete .ost file, etc.

If the intention is to keep this mailbox to meet legal requirements, just use the Inactive mailboxes functionality: http://technet.microsoft.com/en-us/library/dn144876(v=exchg.150).aspx [http://technet.microsoft.com/en-us/library/dn144876(v=exchg.150).aspx]

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I have download a mailbox that resides on 365, I wanted to back up the mailbox so I exported including sub folders to PST , I then open the PST file to compare but the number of emails in the inbox and set item are different in the PST to the actual mailbox which I find strange. &nbsp;Any ideas advice, I am backing this up before converting to a shared mailbox in 365.
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I have download a mailbox that resides on 365, I wanted to back up the mailbox so I exported including sub folders to PST , I then open the PST file to compare but the number of emails in the inbox and set item are different in the PST to the actual mailbox which I find strange.  Any ideas advice, I am backing this up before converting to a shared mailbox in 365.

Outlook

Office 365 is a group of software plus services subscriptions that provides productivity software and related services to its subscribers. Office 365 allows the use of Microsoft Office apps on Windows and OS X, provides storage space on Microsoft's cloud storage service OneDrive, and grants 60 Skype minutes per month. Office 365 includes e-mail and social networking services through hosted versions of Exchange Server, Skype for Business Server, SharePoint and Office Online, integration with Yammer, as well as access to the Office software. All of Office 365's components can be managed and configured through an online portal; users can be added manually, imported from a CSV file, or Office 365 can be set up for single sign-on with a local Active Directory using Active Directory Federation Services.

Microsoft 365

The term "Backup" means the methods and processes involved to copy computer data (system data as well as application data) to media other than the ones where the data originally live (disk, tape, optical, cloud). "Restore" in turn means the methods and processes involved in data recovery, i. e., bringing back copied computer data to their original location. Backup/Restore primarily serves as a means of protection against data loss, be it due to disaster, corruption or sabotage. It can also be used for recovering data from an earlier point in time and even for cloning machines or applications. There is a wide variety of backup/restore software available, from expensive commercial products to free or open source tools.

Storage Software

Microsoft Outlook is a personal information manager from Microsoft, available as a part of the Microsoft Office suite. Although often used mainly as an email application, it also includes a calendar, task manager, contact manager, note-taker, journal, and web browser.