Peter Fury masterminded his nephew Tyson Fury's stunning win over Klitschko in December 2015, a result that blew the division open after 11 years of dominance by the giant Ukrainian.
Now Peter Fury is hoping his son Hughie will beat WBO champion Parker in Manchester on Sunday (NZT) and return the belt to the family.
Peter Fury might have been rudely dismissive of Parker's promoter David Higgins in an expletive riddled send-off as they argued over the British referee controlling this fight, but he had nothing but praise for the 25-year-old New Zealand boxer.
Peter Fury said Klitschko's style had become predictable but Parker presented something of an unknown quantity.
"Parker's young, rough ... in a lot of ways he's more difficult as you don't know what's coming," Peter Fury told the BBC when asked to compare the two world heavyweight title fights he's been in charge of.
But Fury felt Hughie was up to the task on top of what had been a demanding training camp.
"I've prepared Hughie for 12 rounds of a tough contest. We are taking nothing away from Joseph Parker, we've always said he's a good fighter," Peter Fury said at the general press conference in London.
"But Hughie has had a camp where he has prepared for wars. He's been hit a lot, he took a lot of punishment in sparring, 12 rounds three times a week, sometimes 15 rounds, changing sparring partners. He's been battle-proved and this is a war as far as he is concerned.
"And good luck to him, anything can happen in boxing and this is what we have prepared for. It's going to be a very good fight between two up and coming heavyweights."
Hughie backed up his father's faith, saying: "This is the best training camp I've been involved in.
"Believe me, I'm bringing that belt back home because I've put all the hard work in. This is going to be an unbelievable fight; you've got two young hungry fighters who want it more than anything. It's a matter of who wants it more because I'm willing to die in that ring. I just can't wait now to get in there and do the job.
"I'm super confident in my ability and my fitness. No-one has seen anything like the new Hughie Fury," he added as he gets set for is first fight since April last year.
"The lay-off doesn't mean anything. I feel great, I've done all my training. I'm so fit and mentally fit.
"Joseph Parker's a good fighter but he's going to bring the best out of me."
Photot by: MATT IMPEY/PHOTOSPORT (Caption: WBO heavyweight champion Joseph Parker (left) and challenger Hughie Fury during their title fight press conference in London).