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As a company we are using Office 365 and as such on our PC there is an OST file allowing users to access their Outlook Email even if they are offline. These files can get quite large so if a user gets a new PC what files can be copied to the new PC to reduce the time is takes outlook to sync to the cloud the first time it is opened on the new PC ?
The OST file is contained in folder C\Users\<uname>\AppData\Local\Microsoft\Outlook\
The question you're asking is actually about the Outlook client software, rather than Exchange Online. I'd recommend contacting the Outlook team from the Outlook forums to address this question.
That said, there's already an article up about this on the Office help website: