I'm not sure if you have tried BITWARE (Fax Software). We have been using this for a long time. It works fine.
You have first to set up a "virtual modem" in you laptop using Nokia Data Suite. I'm not certain, however, if 6360 is supported. Once it's OK, BITWARE will then utilize your "virtual modem" for sending and receiving faxes.
Always remember that you have to subscribe the "DATA/FAX" services from your network provider.