Hi Abdulhaq,
According to your description, I understand that you want to sync the mailbox items from a user's Mac machine to the Exchange Online.
Before moving on, I'd like to confirm whether you actually mean the .OLM file when you mentioned the pst. Because based on my knowledge, the Outlook 2011 for Mac is using the .OLM file to export/import mailbox items.
And here are the recommended steps to sync items to a Cloud mailbox.
1. Export all items to a .OLM file. (If you already done it, just ignore this step.)
2. Set up the Office 365 mailbox in the Outlook 2011 for Mac.
3. Import the .OLM file into the O365 account.
Then O365 will sync the items from local to the Cloud.
If there is anything unclear, or I have misunderstood you, please don't hesitate to let me know.
Thanks,
Henry Huang