I have always used Outlook for PST.  

I back up my *.PST files and carry them with me on a USB.  

I recently purchased a Mac Air and Office for Mac 2011.  I am aware that MAC uses a different format (*.olm) for Outlook, and that it is difficult to export OLM to PST without specific third party software. 

I have decided therefore to keep my PC as the primary user of Outlook and to have my PST files converted to Outlook for MAC so that they are available on my MAC (mainly for reference).  If I do choose to send an email, add a contact or insert a calendar entry from the MAC, I send it by email to a second email address so it can be updated on my primary PC later on.

Here is the question - apologies for the long pre-amble...

I want to keep updating the MAC with my new PST file, but I understand that it is not as simple as deleting the OLM file and re-importing the PST file, because the OLM file does not appear to exits on the MAC.  Instead apparently everything is held in something called "Identities."

Can I please ask an expert whether there js a way that I might accomplish the above task?  

Do I delete "Identities" and then re-import the PST?  Do I have to delete all of the information within Outlook and re-import (as that would be very cumbersome).

Why on earth MS could not make their own software cross-platform, I do not know.  They appear to have made the interface between Outlook 365 and Outlook.com even more complicated.

I very much appreciate those of you willing to give up your time and share your expertise.