@gmayor: Thanks for your answer. Do you mean like double-click and let the software do its magic? Unfortunately, this doesn't work on Mac or at least not on my machine. I have tried that but nothing happened, then I clicked "Open with.." and chose "Outlook", but this will only open a new email addressed to the email address of the .pst file.

What happens when you go to File > Open & Export > Open Outlook Data File?

No, Graham means putting the PST in the location where Outlook looks for the 'Data File' to use. I have no clue re Outlook for Mac either, but this is a simple 30-second task on PC—put the PST in the right place, and tell Outlook to use that PST as its "Data File".