We have a thread that lists specific current known compatibility issues here:
Express Card To PCMCIA adapter compatibility Currently there have been some people having problems with using the adapter with the HP 1000 series laptops. This would also include the 1320 laptop. So basically, it might work, but it might not. At this point there are some issues, but not everyone seems to be having those same problems. You can take a look at the link above for some more info.
If you have any other questions let us know.