In this case A would be at an advantage to spend the 2 minutes looking for the next block. If they happen to find another block quickly they could release then in quick succession.
The benefit there is that if another miner released a block before that 3 minutes this miner still can release their first block and has already spent 2 minutes working on a block that could better validate their first block now that there are competing chains.
The benefit there is that if another miner released a block before that 3 minutes this miner still can release their first block and has already spent 2 minutes working on a block that could better validate their first block now that there are competing chains.