A large, fleshy plant that blooms with large, lotus-like flowers. My friend says her mother told her it was a Christmas cactus, but I don't think so. I have had many of those through the years and they are not so big as this one. It is very large.
I have tried to propagate it from one "leaf" (don't even know what to call it!), but not successfully so far.
This is one of the ugliest of all plants, until it blooms - it's known as the Orchid Cactus or Epiphyllum - and your friends mother is right, in a way, as this is related to the Christmas Cactus which is called Schlumbergera. They require the same care, as they are both epiphytes and originated growing high in the tree tops in temperate jungles.
It looks like your plant is quite happy with the care you've given it.
To propagate, it's important to allow the cut surfaces of the leaves to callous, or dry out. Then they'll root within a few weeks.
Happy Orchid Cactus Growing!
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