Sorry, but what sounds fine in theory is simply not in return correct.
I have to admit that I have no official source, but from all we know, Saturn was asked to develop especially for the J-10 a new version .... As such the FN was especially designed as a J-10-tailored version for CAC. In the same way You can't fit a GE F110 used in the F-14B to a F-15 or F-15S it's also here: You can't fit a FN into a Flanker or a F into a J-10.
The fact alone that China is able to overhaul its engines independently and reassemble them does not mean they switch or even that it is possible to rebuild a F as an FN and vice versa.
By the way it's indeed the first time I've heard this ... and I've already heard a lot ...