FWIW, if you have a CX segment in your itinerary then on the CX web site you can apply your FF number, in my case BAEC number, to the entire itinerary. Note the the ticket does not have to be issued by CX, most of mine are issued by AA, and a few from BA, and AA occasionally screws up the FF number so I always (when I have a CX flight in my itinerary) go to CX web site and apply my BA FF number to the entire itinerary and it has always worked like a charm.

Their web site has changed a bit since the last time I had an itinerary that included CX (pre-Covid), so just go to Manage Booking and click or find a booking as a guest on the right and enter your name and Record Locator/PNR. Hopefully they still have this capability, but I don't have an itinerary with a CX flight right now so can't provide further instructions on how to get to where to make FF number modifications; perhaps someone else can provide more details and/or let us know if this capability still exists.