Wendy - thank you for your response. I've been reading up on Schlumbergera since your post, and still am not sure. May I ask what distinguishes it or how you thought of that genus?
I see what you mean - I've never been at this house in June-July, which should be when this blooms down in Australia?
Thank you Douglas. I've been looking at photos on line. Everything looks so much alike. Do you know when Hatoria would bloom in the Southern Hemisphere?