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The 67-year-old adventurer has now rowed more than 3500km from the coast of Dunedin.
His son, Oscar, said Mr Konyukhov was expected to cross the halfway mark on February 6.
''There are many intermediate records already.
''Fedor is the oldest solo rower ever at sea; he entered 49 degrees south - the deepest south ever on a solo rowing attempt; and by February 6 he will be the only person in rowing history to spend 60-plus days in the Southern Ocean on a rowing boat.''
Mr Konyukhov is about to leave the New Zealand Maritime controlled zone and enter the Chilean sector of the Southern Pacific Ocean.
In his latest communique, he said gale-force winds, rain and 10m swells had been causing him difficulty, but it had now cleared and he was able to bring the cabin and boat back into order.
''I weathered the storm without any breakdowns. The wind was strong, but northerly, meaning that it was warm.
''It created huge waves, but the boat is sturdy and she withstood it all.
''I noticed again today that the hull is becoming overgrown with seaweed and barnacles, and little fish come to nip at the bottom.
''I haven't seen any large mammals [dolphins and whales], but the sight of the little fish brings me joy.''
His row to Cape Horn is the first of three legs in his 27,000km journey from Dunedin, past Cape Horn, South Africa, South Australia and back to Dunedin.
He will begin his second leg in December 2019, from Cape Horn to Cape Leeuwin, in Western Australia, and the third will begin in December 2020, from Australia back to Dunedin.
Each leg is expected to take about 120 days.