The 30 days' extension of time - the second 30-day appeal extension in the case - was granted on Monday, Phuketwan has learned.
It followed a letter from prosecutor Miss Pattathira Bhumisutthapon to Phuket Provincial Court, dated October 27.
In December 2013, the Royal Thai Navy initiated criminal defamation and computer crimes charges against journalists Alan Morison and Chutima Sidasathian and Big Island Media, Phuketwan's parent company, over word-for-word reproduction of one paragraph from Reuters news agency on July 17, 2013.
Charges have not been brought against Reuters or the two news agency journalists who wrote the paragraph, or against other Thai news outlets which reproduced the same information.
Reuters and two of its journalists later won a Pulitzer prize for a series of features on the Rohingya boatpeople in which the paragraph was included.
The two Phuketwan journalists have been reporting on human trafficking in Thailand and the treatment of stateless Rohingya and Bangladeshis since 2008, with their exceptional work noted in several international awards.
Many well-regarded international organisations spoke out against the charges, urging Thailand's military government to intervene and end the prosecution.
The Phuketwan journalists faced a maximum of seven years in jail but on September 1, a judge at Phuket Provincial Court dismissed all charges.
Six weeks earlier, the three-day trial had been told that the case had been based on a poor translation from English into Thai, that the Computer Crimes Act was intended for use against hackers and data thieves, not journalists, and that the Navy had failed to demonstrate that its reputation had been damaged.
On October 29, senior Royal Thai Navy officers met in Bangkok and decided not to lodge an appeal over the verdict dismissing all charges against the journalist and the company.
The Navy had been granted an extra 30 days on top of the initial 30 days in which to consider an appeal.
On October 30, a letter from the Royal Thai Navy informed the Phuket Provincial Court of the decision by the service not to appeal.
Three days earlier, the Phuket Prosecutor's office had lodged its request for an extension of 30 days from October 31 in which to consider an appeal.