The South Carolina Court of Appeals has granted Alex Murdaugh's motion to suspend his conviction appeal and sent the case back to circuit court to consider allegations of jury tampering by the Colleton County clerk.

The decision clears the first step in the quest for a new murder trial by the notorious South Carolina fraudster who was convicted in March of murdering his wife and son.

Chief Judge H. Bruce Williams signed the order Tuesday morning.

The case is now remanded to circuit court to consider the jury tampering allegations.

"The recent ruling to stay the appeal and remand the case for a hearing on Alex Murdaugh's motion for a new trial is welcomed news," said Murdaugh's attorneys Dick Harpootlian and Jim Griffin in a joint statement to CNN.

"We intend to proceed expeditiously and will seek a full blown evidentiary hearing addressing the serious allegations pertaining to improper jury communications by the Clerk of Court."

The South Carolina Attorney General's Office told CNN they would "respond through the legal process at the appropriate time."

Murdaugh, 55, appealed days after he was convicted following a six-week trial of shooting and killing his wife, Maggie, and grown son Paul at the family's hunting property.

He is currently serving two consecutive life sentences in a state prison for their murders.

Murdaugh pleaded guilty to nearly two dozen fraud and money laundering charges last month in a federal courtroom in Charleston.

The plea was related to a scheme in which Murdaugh and a bank employee allegedly defrauded his personal injury clients and laundered more than $7 million of funds, according to an indictment. Murdaugh was accused of using the settlement funds for his "personal benefit, including using the proceeds to pay off personal loans and for personal expenses and cash withdrawals."

The cases brought national attention to Murdaugh, a former personal injury attorney and member of a dynastic family in the region, where his father, grandfather and great-grandfather served as the local prosecutor consecutively from 1920 to 2006.

Murdaugh's attorneys last month filed a motion to suspend that murder conviction appeal so they could move forward with requesting a new trial.

Their motion contained allegations that Colleton County Clerk of Court Rebecca "Becky" Hill "tampered with the jury by advising them not to believe Murdaugh's testimony and other evidence presented by the defense, pressuring them to reach a quick guilty verdict, and even misrepresenting critical and material information to the trial judge in her campaign to remove a juror she believed to be favorable to the defense."

CNN has reached out to an attorney representing Hill for comment.