It has been over a year since I considered that problem, but the last I knew there was no way.
Microsoft has a vested interest in NOT allowing any other products (free or not) to manage files from MS products properly. We went through 11 years of issues to get Word documents working, and MS is still trying to obfuscate things. They have NO incentive to make this easy.
In addition (and possibly related to the above) the PST file format has undergone a recent revision that requires a conversion step in moving from 2007 to 2010. Since few people are working on it, they are getting NO help from MS, and they are aiming at a moving target, I doubt if things have improved greatly.
Arguably the BEST way to use any mail client is using a standard protocol that leaves the mail (or a copy) on the secured mail server. You can change clients and see exactly the same mail. Alternatively and if that is not an option, backing up mail to a PORTABLE format is not a stupid choice!
I really hope that I am wrong on this and that someone HAS solved the problem. If not, all I can do is wish you the best of luck and share with you these links:
I also found a comment (on another forum) indicating that you CAN import it directly, but you need to have the VERY LATEST evolution and may have to try multiple times. Another thread mentioned that the folder in the PST that you import must have ONLY mail, no subfolders. Try and manage THAT without windows! Another mentioned duplicates generated with each attempt at import.
The readpst project had great promise (converted PST to MBOX format), but it seems to have stagnated and I am not sure it is still alive.
Personally, I gave up.