Cher and her lawyers say Mary should pay the bill because she tried to "misuse" the termination provisions of the Copyright Act to illegally "obtain a windfall" at Cher's expense.
They claim Mary then "dragged this case out for five years by taking patently unreasonable positions".
In the divorce settlement, Sonny had assigned Cher a 50 per cent share of his composition royalties for hit songs including I Got You Babe and The Beat Goes On. Cher also got a 50 per cent share of the musical recordings they made together.
Cher's grant was untouchable, the judge found.
"Defendant argued, repeatedly and frivolously, that a federal statute that expressly states it does not affect state-law rights somehow extinguishes those state law rights," the new motion for legal fees states. "Cher prevailed completely."
Cher's new motion for fees says she was forced to run up a bill of $1,023,605.50 (£762,641.17) with her lawyers to successfully defeat Mary's "improper attempt at termination".
