This claim will be judged as a Yes if at any time between January 20, 2009 and December 20, 2012, presidential power in the United States of America is transferred to any individual other than Barack Obama for a period exceeding 30 consecutive days.
The claim condition says that (the claim is true if) powers are transferred TO someone other than Barak Obama. It doesn't say anything about who they must be transferred FROM, so I read there being no such requirement. To be specific, if presidential powers are transferred from Bush to Joe Biden on January 20, 2009, and he remains in power for more than 30 days, then the literal wording of the claim is TRUE and would be judged as such. On the other hand, if Joe Biden takes office on January 19 2009, and remains in office for the full term, the claim is FALSE.