Do you have one of the lines on the Partner system dedicated for incoming faxes? Just program the extension that the fax is connected to for immediate ring on that line only.
If you share a line for incoming voice calls and incoming fax calls, you're going to have to answer first and determine if it is a voice call or a fax call. If fax, then transfer to the fax extension (you can use an auto-intercom button to do this). Program the fax extension for no ring, or delayed ring to be able to receive unattended at night. OR, no ring, assign to the Night Service group, and Outgoing Only for all lines except the fax line, and press the Night Service button to receive automatically at night.
If you use an auto attendant to answer calls immediately, put the fax extension in hunt group 8, but with no ring, and the system will listen for CNG tone on incoming calls, and automatically transfer for you.