Saving users from bad migration. Import .pst file to office 365

Hi 

I'm trying to help a customer, saving all the mess after another commpany made a very bad office 365 migration. 
A lot of things didnt went out as the users thought it will go. 

But one of the worst is that they are missing many emails from their archive folder on the old system. Luckily i have found a backup of the archive.pst files from all users on the server.
But.
When i try to import the pst files from file->open->import and then import the .pst into the mailbox, it goes well at first sight. When i return to the same folder 10-15 minutes later, the folders are empty and there is no mails inside. 

This is hardly my first experience with the office 365 and my guess would be that it some how "sync" the local outlook content with the "cloud" content.- But that the cloud content overrules the local content and thereby deleting it again. 


So.. first of all - whats the right way to import a pst file into a mailbox in o356? 

Secondly - am i right in my theory?! ;) 

Thanks in advance 

/Jesper