On December 21 "the defendant reported into the police station and admitted that she had made up the allegation because she wanted him to stay in jail longer", Judge Lynch said.
King has pleaded guilty to making a false statement.
She also pleaded guilty to two counts of theft, the first being a bag of confectionery and an item from the beauty aisle of New World supermarket in November, and the second being a theft of a friend's benefit money in January.
The victim did not have a bank account for the money to be put into, so arranged for it to be put into King's account.
When they went to withdraw the money, however, King told the victim neither of their benefits had come through.
In reality, King had transferred the money to a different account, which she would not reveal to police.
She told them the money was spent on P, Judge Lynch said.
During her sentencing on Thursday, defence lawyer Stephen Ross said King suffered from a disability that "causes her difficulties with offending".
Judge Lynch said King had four previous dishonesty convictions, and a "lenient approach" had been taken with her in the past.
He said the reason, which "sounds uncharitable" but "puts matters in context", was that King "operates at a low intellect".
"I make it plain, Ms King, that to continue to be dishonest will result in the court going further up the ladder in terms of its responses."
Judge Lynch said he would sentence her to community detention this time, but next time the "discussions" would be around a term of imprisonment, possibly lessened to home detention.
"The false statement is aggravated by the potential putting the ex-partner right in the frame of very serious offending.
"This charge ought to have a greater sentence available to it than the maximum of three months."
He also described King taking the other victim's benefit money as "particularly mean".
He sentenced King to three months of community detention and nine months of supervision, ordering her to pay reparation of $210 for the stolen benefit.
