AH Challenge: Make Austen Chamberlain Prime Minister of Great Britain

The POD is 1903 or later. Here is the wikipedia entry about Chamberlain: http://en.wikipedia.org/wiki/Austen_Chamberlain .

He withdrew from the contest for the Conservative Party leadership in 1911 and Bonar Law became leader. If he had become leader in 1911, he would probably still be leader in 1922.

In OTL he became Conservative leader in 1921 when Bonar Law resigned because of illhealth. He was in favour of maintaining the coalition with Lloyd George and resigned as leader when Conservative MPs voted by 187 to 87 at the Carlton Club meeting on 19 October 1922 to leave the coalition. With Chamberlain as leader since 1911 would Bonar Law have been in a position to become leader in 1922?
 
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