Name	Lifeboat from Titanic	Lifeboat to Carpathia	Confidence Level
Barkworth, Mr Algernon Henry Wilson	Collapsible B	12	5.00

An April 16 account given to Carpathia passenger Mrs. Cecil Francis states:
“I climbed up on the boat deck railing and dropped about 30 feet into the sea. …..  Looking over my shoulder I saw the Titanic disappear with a volley of loud reports so I swam slowly around and came luckily up on an upturned lifeboat.”

Hull Daily Mail, May 17, 1912:
  “The lights of the vessel had disappeared one by one as she sank, and I continued to swim in the darkness. Suddenly I saw ahead of me what proved to be an upturned lifeboat of the Titanic with a number of people standing on it. I swam up to this, and got hold of it while there were shouts of, “Look out, you will swamp us.” Naturally I did not pay much attention to these, but managed to draw myself up to the side of it."

Archibald Gracie’s book The Truth About the Titanic agrees Barkworth was on Collapsible B, and adds the additional detail that Barkworth came off Collapsible B into the same lifeboat he and Lightoller did, #12.   From Gracie:
  "In the lifeboat to which we were transferred were said to be sixty-five or seventy of us. The number was beyond the limit of safety. The boat sank low In the water, and the sea now became rougher.  LIghtoller assumed the command and steered at
the stern. I was glad to recognize young Thayer amidships. There was a French woman in the bow near us actively ill but brave and considerate.  She was very kind In loaning an extra steamer rug to Barkworth, by my side, who shared it with a
member of the crew (a fireman perhaps) and myself."

So, the lifeboat he was saved by was Collapsible B, and he subsequently got in #12, along with Lightoller, Gracie and Thayer.