Arnall, 58, deposited the cheque after earlier this week declining the payment and pledging to pursue her appeal of a divorce ruling she viewed as unfair.
In the November ruling by an Oklahoma County Court judge, Hamm, the chief executive of Continental Resources was allowed to keep his 68 percent stake in the firm, now worth about $9 billion, while Arnall was awarded about $1 billion in cash and assets from the marital estate.
The cheque represents the entire remaining balance of what Hamm owes Arnall based on the November ruling, including interest. The oilman's divorce lawyer, Craig Box, said he believes Arnall's deposit of the cheque will end her efforts to appeal the case and that Hamm also wants the case resolved.
"We have received confirmation that the cheque was deposited in an Oklahoma City bank," Box said. "We feel this is the end of the case from her perspective. It means she's done and should dismiss her appeal."
A person familiar with Arnall's case confirmed the deposit, which represents one of the largest divorce awards in US history. Arnall could not be reached directly for comment. It was not clear whether she intends to pursue an appeal after the cheque clears.
"If she's cashing the cheque, I would think the reasonable conclusion is that they both will accept the trial court's decision, dismiss their appeals and put an end to the case," said Oklahoma family law expert Carolyn Thompson.
Earlier, Hamm had filed his own appeal, seeking to have Oklahoma's Supreme Court reduce what he owes Arnall, after a plunge in oil prices shaved billions from the value of his Continental shares in recent months. During a trial last year, the shares had been worth as much as $19 billion.
The Hamm case, initially filed in 2012, has pitted Oklahoma's most successful oil wildcatter against his former wife of 26 years, an attorney and longtime executive at Continental. The firm, a leading oil driller in North Dakota, was dragged into the case but has said it did not affect business.
In an appeal document, Arnall contended a trial judge wrongly allowed Hamm to keep more than 90 percent of the wealth the couple accrued during their marriage.
Although Hamm owned Continental before the marriage in 1988, the value of his shares surged 400-fold during the union. Arnall has been seeking a multi-billion dollar portion of those gains.
To limit what he would owe, Hamm's defense sought to show that his company's growth during the marriage resulted mostly from "passive" factors beyond his control, such as rising oil prices. Under Oklahoma law, only the growth in wealth stemming from the active efforts and skills of either spouse during the marriage is split in a divorce. Arnall contended that Hamm's deft management of the firm led to its growth.
Hamm has already paid Arnall more than $20 million during the case, and the parties have spent millions in legal fees.