I believe the inability to import Contact Groups from Outlook is a known issue/limitation of the Import Wizard.
I don't have an exact answer for you on how to proceed. However, I just did some testing on my account with the format of the .csv file used in the Import/Export contact function on the Options --> Address Book. I exported my Address Book, which includes one Contact Group. The first line of the .csv file contains all the field headings. For the Contact Group all the names and e-mail addresses are saved in the "dlist" field. The "type" field is populated with the word "group". An example of the format of the "dlist" field is as follows:
If you can somehow get your user's contact groups into this format you should be able to import them.
"""John Doe"" <firstname.lastname@example.org>, ""Jim Jones"" <email@example.com>, ""Bill Smith"" <firstname.lastname@example.org>"