Name	Lifeboat from Titanic	Lifeboat to Carpathia	Confidence Level
Avery, Mr James Frank	Collapsible B?	4? or 12?	1.95

The New York Call of April 20, 1912 said Frank Avery (a trimmer) went down with the ship and clung to a piece of wreckage for ninety minutes before being picked up.

Jack Thayer, The Sinking of the S.S. Titanic,:
   "About twenty of our whole group were stokers."

Archibald Gracie, The Truth About the Titanic, statement by 2nd Officer Lightoller:
    "Eventually, about thirty of us got on it: Mr. Thayer, Bride, the second Marconi operator, and Col. Gracie. I think all the rest were firemen taken out of the water."

It appears on the minimal evidence we have, that Avery may have climbed up on Collapsible B, with Gracie and Thayer.  And if he was on Collapsible B, then he would have transferred to either of #4 or #12.