There was less than 36 hours between Sir Alex Ferguson announcing his decision to retire and Moyes' appointment as Manchester United's new boss, underlining the speed with which the United hierarchy wanted to get the succession issue settled.
For Kenwright, the process is going to take slightly longer.
Wigan's Roberto Martinez has already been ousted as favourite by Neil Lennon, whose performances in the Champions League with Celtic this season offers an experience at the highest level even Moyes cannot match.
However, such is the mature manner in which Moyes has handled his own exit, his relationship with Kenwright remains strong enough to have significant input, just as Ferguson did in United's decision to go after his fellow Scot.
"I'll help Everton as much as I possibly can," said Moyes.
"Walter Smith recommended me for the job here and if there is anything I can do to help Bill Kenwright with what happens next I will be more than happy to do so.
"It is a great opportunity. Everton is a well run club and we don't get ourselves into too much trouble.
"There is a brilliant training ground and a great set of players with a terrific attitude.
"Whoever comes in is coming into a really good environment."
The situation is different to the one he inherited 11 years ago.
Though Moyes offers Smith the credit for stabilising a club who had flirted with relegation far too often, he needed to ensure the Merseyside outfit were consistently pushing towards the top end of the table.
He has managed it too, and would be hot favourite to land a European spot had clubs from outside the top five - Swansea and Wigan - not managed to win the Capital One Cup and reach the FA Cup final respectively, claiming those Europa League berths for themselves.
"When I took over we were bobbing along not far off the bottom of the Premier League," said Moyes.
"Now, it is a club that, on Sunday, will still be competing to be in Europe. That is a big thing."
It is one of the reasons why there was never any real doubt Moyes would be able to complete the final two games of the campaign, despite announcing he was joining a club Everton fans have not always been well disposed to.
The last player to make the switch to Old Trafford from Goodison Park, Wayne Rooney, received tough receptions whenever he returned - he was even abused by a sponsor on one occasion - although, after nine years, the ire has now quelled.
For Moyes though, it was important his exit was handled properly, and to that end, he has done a superb job.
"Hopefully on Sunday the fans will react in the same way they did when I first stepped through the door," he said.
"You can never tell with football fans. They support their team and I would understand it if they weren't happy.
"But I will be standing in the same position as I always have done, trying to see if we can keep everything focussed and moving in the right direction.
"The fans have always been great to me. It is 11 years since my first game against Fulham but I remember it as though it was yesterday.
"I was a relative unknown coming from Preston, but they got behind me.
"It's not normal nowadays that a manager stays in their job for 11 years. If I hadn't had their backing it wouldn't have happened."
And so Moyes prepares for what he calls a "short cheerio", knowing the emotion that will come from all sides of a famous old stadium.
"I really enjoy the people I work with," he said. "I enjoy Goodison.
"It is an old lady of a football stadium, which can be raucous on its day.
"It has been such a big part of my life. But another way of looking at it is that I might have been sacked and the whole story would have been different.
"I think you accept as a manager that, at some time, you are going to have to leave.
"I always hoped that when I left Everton I would be able to walk back through the front door."