The cold case has gripped the nation and grew in momentum following the release of the critically-acclaimed podcast, The Teacher's Pet.
The 36-year-old mystery concerns the disappearance of Lyn Dawson from her home on the Northern Beaches of Sydney in January 1982.
Her husband Chris Dawson, a former PE teacher, moved his schoolgirl lover into the family home just days after his wife went missing.
Comm. Fuller said two additional witness statements had been taken since April, but would not comment on the significance of that evidence.
"They were predominantly statements from witnesses that helped us tie pieces of the puzzle together", he said.
"We won't give up on trying to identify the whereabouts of Lynette Dawson, but, from our perspective, it is not crucial to finalising the matter".
A spokesman for Chris Dawson's family said they are "disappointed" in yesterday's explosive developments, and claimed there was "clear and uncontested" evidence Lyn was alive long after she disappeared.
While appearing at Southport Magistrates Court on Wednesday afternoon, he sat quietly looking at the floor, trembling at times with his shirt visibly shaking as he breathed.
The commander of the NSW homicide squad, Detective Superintendent Scott Cook, said he was "confident" in the case.
Dawson continues to maintain his innocence. Inquests previously recommended murder charges against a known suspect, though prosecutors decided there was insufficient evidence.
Paul Dawson applied for bail, promising to drive himself to Sydney for the court appearance.
Dawson was hoped to be extradited to NSW on Wednesday, however police were unable to organise air transport for him out of Queensland.
New South Wales Police's Strike Force Scriven was established in 2015 to reinvestigate the case.
"It's my understanding that there were two additional statements that were a by-product of the media and the work that the media has done".
It came after Mr Dawson began a relationship in 1980 with his 16-year-old student Joanne Curtis.
Detectives in September dug up the backyard at the Bayview home the couple shared in the early 1980s but did not find her remains or items of interest.
"We have to also ensure Chris gets due process".
"We have sold homicide before without identifying the body", he continued.
"We've had a cry, we've cuddled, we're just completely over the moon that something has finally happened", he told The Australian.