READ MORE: Frustration as families try to get bodies home
The two students, Mr Hollnsteiner, 21, of New York, and Mr Murphy, 20, of London, died on September 25.
They were part of a Monash University in Melbourne group visiting New Zealand during a break.
Speaking from New York yesterday, Mr Hollnsteiner's mother Ria David said she hadn't yet been able to make funeral arrangements to farewell her son, nine days after his death.
"He's not been released yet. We do have a funeral home in New Zealand but he's in hospital. The coroner won't release him yet."
Mr Hollnsteiner's body was to remain in New Zealand while identification procedures were carried out.
The family was in contact with the United States consulate in Auckland, but Ms David said the wait was frustrating.
"We just want our son back," she said.
"Family members are already flying in for the week for the funeral and they are coming from the Philippines and California - all over. I'm hoping for next week."
Ms David said she'd spoken to Mr Murphy's parents, John and Sue Murphy, and they were also waiting for their son's body to return.
She understood Mr Murphy's body had been identified but wasn't going to be released until Mr Hollnsteiner's body could be.
Nine other Monash students were on the lake at the time. They returned to Australia last Sunday.
The group of 11 was travelling around in campervans and on the fateful Friday went to the lake for the day and hired kayaks.
Tragedy struck when the group ended up in icy water. They were tipped in when a gust of wind caused a swell.
READ MORE: Two dead, nine injured at Lake Tekapo</strong>
All 11 were wearing life jackets and Mr Hollnsteiner and Mr Murphy were thought to have succumbed to hypothermia.