Mary Jane is upset about the slaves being sold (families were broken up).
Huck, overcome by her misery and, more importantly, her beauty, breaks down and confesses everything to her.
Together they devise a plan. Or rather, Huck devises a plan and Mary Jane goes along with it.
The plan is, Mary Jane goes for the night to stay with Mr. Lothrop, because the girl's got the poker face of a five-year-old with a sugar high. (In other words, she wouldn't be able to hide her emotions from the duke and king.)
Huck says someone else's life hangs in the balance here (Jim), so he needs time to escape before the situation plays out.
Later that night, Mary is going to sneak back to the house and shine a candle in the window. If Huck doesn't show up, he's escaped, and she can blow the whistle all she wants on the two frauds.
Huck then takes a piece of paper and writes down "Royal Nonesuch, Bricksville," so the duke and king can pay their dues for that little scam as well.
He also writes a note about the money being buried in the coffin, and tells her not to look at the paper until she's already on the road to Mr. Lothrop's.
So, Mary Jane is off—and Huck runs into the other sister, Susan.
He doesn't want to trust someone else with the details, so he just makes up a story about the mumps, a really horrible strain called pluribus-unum mumps.
Lie, lie, lie: in the end, he makes sure Susan isn't going to say anything to the duke and king about her sister's absence, since she doesn't want to delay their trip to England with their uncles while everyone sticks around to see if Mary Jane contracted pluribus-unum mumps.
And then two men show up: the real brothers of the dead Peter Wilks.