Of course, Jennifer had to lie to her mother. Sort of.
Jennifer did indeed have Jon's memories and she knew what he knew.
Which means that she knew that her current situation was the result of a wish and that the KMS was just something invented by the stone to make reality consistent.
And she also knew exactly what Jon remembered about his relation to Jennifer--nothing at all until he read the pamphlet.
She told her mother that Jon was reluctant to change and didn't want to let her out. But Jennifer knew that that wasn't really true. It was a new reality created by the stone. Jon had never really changed at all until now, and the one time he changed he didn't know about it until it happened--there was no question of being reluctant.
Still, there had to be a better solution to this without just her being Jon all the time. And on the way to the party, she came up with something.
After she got there, she explained it all to Liz.
"Kelper's Metamorphic Syndrome?" said Liz. "Okay, now that's a strange wish result. And everyone except you, me, and Karyn think it's a perfectly normal thing.
"But I have some ideas about how to fix it. I mean, I don't want to just change to Jon forever. But there's still something I can do. Hold on, I'm going to make a wish...."
"Okay, I hope you know what you're doing, Jen."
"I wish that there's a partial cure for Kepler's Metamorphic Syndrome. I wish that that after getting the cure, Jon or I will be able to split into two people at will and be Jon and Jennifer at the same time. I wish that we can stay split for up to a day or until we agree to combine. I also wish that once we combine we both keep the combined memories of each one and that the memories don't uncombine when we split again. And I wish that Jon and I get along with each other and are closer than brother and sister."
Jennifer concentrated. Nothing happened. "Huh?" she said.
"What?" said Liz.
"I was trying to split in two."
"Silly!" said Liz. "You wished that a partial cure exists and you wished for what happens when you get it. But you never said you did get it."
"Okay. I wish that I have an appointment for the cure I just described, tomorrow at 10 in the morning."
The next morning, Jon/Jennifer's mother woke him--he was Jon again by then. "Today's the big day," she said. "We're going to the clinic, you know. You'll be able to talk to Jennifer face to face instead of transforming...."
Jennifer hadn't specified exactly what the cure was. So the details were a surprise to Jon. After he went into the back of the clinic to see the doctor, the cure started with....