Or maybe not...?
How can you doubt? Where has he failed to accomplish his objective? Once Goering's Luftwaffe has airfields in France it will sweep the RAF from the sky in short order. The invasion will be, not a piece of cake, but managable under the Luftwaffe umbrella. It may not even come to that. When France falls, so will Chamberlain. He will probably be replaced by someone a little more realistic, who recognizes that German interests and British are not at all incompatible. Once the English people have seen Hitler's power they may even throw in with him and make common cause against the real enemy in the East.