Howard, who spent four years at United before Moyes signed him for the Toffees, believes the Scot will turn things around with time.
"I think the club will succeed and David Moyes, given the right time, will be a huge success," Howard said.
"David Moyes never takes a backward step. He always believes that he can do the right things.
"He believes in his methods, he believes in the players that he brings to a club and that makes for a really good working environment over a long period of time."
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