Really? How on Earth did the Beatles get influenced by the Monkees then?
Seriously? Just listen to their music. It's virtually identical.
Did you think that may be because the Monkees were copying the Beatles and not the other way around? The Monkees first album came out a few months after the Beatles put out Revolver. Heck, the Beatles hosted a party for the Monkees while they were recording Sgt. Peppers. Heck, the Monkees barely played on any of the tracks on their first or second album. They didn't start playing their own instruments until their third album. They were a group that was put together for a TV show. They didn't really become a band until the end of the Beatles career.
It would be like saying Weird Al influenced Michael Jackson because Eat It and Fat sound like Beat It and Bad.