A funeral service for the father of three was held on December 22, Ms Cozad wrote on Facebook.
Winona Langford's parents, Anthony and Kristine, were both killed in the eruption and her brother Jesse is in hospital being treated for severe burns.
Police have identified the pair believed to be washed out to sea as New Zealand tour guide Hayden Marshall-Inman, 40, and Australian teenager Winona Langford, 17. Their bodies are thought to have been swept into the ocean around the uninhabited volcanic island, Whakaari, or White Island.
The desperate families have had their hopes dashed of ever finding their bodies the search was "suspended".
Police Superintendent Andy McGregor said extensive shoreline and aerial searches had not turned up anything new.
McGregor said "no further items of significance" that may help find the missing have been located.
Police said they remain ready to respond if new information comes to light.
New Zealand Prime Minister Jacinda Ardern has said official inquiries by coroners and work safety regulators into the eruption could take up to a year, and will carry potential criminal penalties of up to five years in jail.
"The disappointing factor for us is that we haven't located Hayden and Winona".
A total of 25 remain hospitalized in critical condition.
'I am writing to ask for a pardon for my actions of a personal recovery'.
Lauren Urey, 32, and her husband Matthew Urey, 36, were celebrating their honeymoon on board Ovation of the seas when they visited White Island shortly before the unexpected eruption.
On Wednesday, police said they would be scaling down search operations for the two people still missing after a volcanic eruption last week, admitting the bodies may never be found.
In a message provided by the families of Lauren, aged 32, and Matthew, aged 36, they passed on honest condolences to the families and friends of those who did not survive this tragic event; saying "our thoughts and prayers are with you".