Argentine footballer Emiliano Sala died of head and chest injuries, when his place crashed into the English Channel last month.
An inquest into Sala's death opened and was quickly adjourned in Dorset on Monday (local time), with no members of his family present.
But family of pilot David Ibbotson are desperate to continue the search for his still-missing body at the bottom of the channel.
Sala, 28, was flying from France to take up his new English Premier League contract with Cardiff City, when the Piper Malibu aircraft disappeared on January 21.
After an extensive search, wreckage was located near Guernsey last week and a body was recovered from the wreckage last Thursday, later identified by finger prints as Sala.
The plane is still underwater and proving difficult to reclaim. A full investigation into the crash is expected to take 6-12 months, although an interim report is expected later this month.
The inquest convened for five minutes, but was adjourned to November 5.
Meanwhile, Ibbotson's family appeared on ITV's Good Morning Britain, where daughter Danielle said her father would not give up looking for her if she was missing, so she would not give up on him.
"If you've got hope, then you shouldn't give up," she said. "He wouldn't stop searching for me."
"We still hope and pray, and hope everyone keeps my dad in their prayers."
A web page raising funds to continue the search for Mr Ibbotson was set up on Friday.
Sala's body was recovered in a privately funded search, which was launched after the initial search was called off three days after the men and their plane went missing.
Although Mr Ibbotson has not been located, poor weather conditions meant a "difficult decision was taken to bring the overall operation to a close", a spokesman for the UK's Air Accidents Investigation Branch said on Wednesday.