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The body of the Wanaka 39-year-old was recovered from the lake on Monday night in a combined effort by police, the navy and coastguard.
On Minaret Station's Facebook page in a letter from Jonathan, Nick and Toby Wallis to "our industry friends and colleagues", the brothers say Matt was "one of four very tight brothers".
"We worked closely and laughed loudly together.
"Matthew left a lasting impression on everyone he met. His warm character and huge smile filled a room. He always took the time to make others feel special."
He was an adored son to Sir Tim and Prue, and above all other things, a wonderful husband to Alice and proud father to Arthur.
"As so many of you know first hand, he was passionate about providing guests from all corners of the globe with the most quintessential of New Zealand experiences. He was an exceptional host and a highly skilled outdoorsman."
The station team was strong and resilient and while they were all equally heartbroken at the news, they were committed to continuing the legacy Matthew helped create at the station.
"He would be furious if we did anything but that."
They thanked everyone involved in the recovery efforts, including the "huge number" of volunteers, including many of Matthew's friends.
Their focus was now on supporting Alice and Arthur.
"Thanks for your many kind messages and your ongoing support."