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The body of Rosalie Anderson-Hill was was found near Summit Rd about 11.30am on Monday.
Police believe the 21-year-old died between October 25 and the morning of October 26.
Detective Senior Sergeant Damon Wells said her death was being treated as "unexplained" while police try and piece together a timeline of her movements.
It was thought she may have had her black globe-brand longboard with her but police had not initially found it and were appealing for information.
However this afternoon Det Snr Sgt Wells confirmed a member of the public had found a longboard and handed it in.
He also confirmed the longboard did indeed belong to Ms Anderson-Hill.
"Police want to thank the public for coming forward with information relating to sightings of Rosalie Anderson-Hill.
"As a result of this information, we now have a greater understanding of Rosalie's movements," he said.
A Facebook group has been set-up for friends and family to share memories of the woman.
It has been inundated with messages since its creation.
"I will always miss you. You were that funny, free spirited, friend I always adored and when we were together we just clicked," one post said.
"Still really don't know what to say. Thank you for being a beautiful part of our lives, you won't be forgotten," another said.
Anderson-Hill's body was located by a member of the public near the Cattlestop Crag.
Wells said police wanted to hear from anyone who was in the area on Sunday, or saw the woman walking in the Mt Pleasant, Lyttelton or Summit Road area overnight on Sunday through to Monday morning.
Anderson-Hill is described as having a slim build, approximately 160cm tall with dreadlocked blonde hair.
She was wearing a dressing gown with a hood, white and blue paisley-patterned long pants and black and white shoes.
Family were reunited with Anderson-Hill yesterday and a memorial service will be held tomorrow before she is buried in Diamond Harbour on Saturday.
Her 21st will also be celebrated belatedly as her birthday fell during lockdown.
Her death will be referred to the coroner, police said.