The jury is out on whether its an Atemoya or Cherimoya and that will also have a hand in how stable the genetics are.
Hasn't it been stated definitively that if it were pure or true cherimoya it wouldn't produce fruit in Florida, so it has to have some sugar apple in its genes?
I haven't seen any genetic test posted here so i can't be 100% sure as to what it is.
I do have my own suspicions but I don't care enough to pay the money for a proper test.
Also, Wayne Clifton, the person who introduced it, claimed it to be a Cherimoya
On a side note, there are a few cherimoyas that fruit here.
Not saying its even worth it but it has been done