Attacker Changing Address to Receive Block Reward

A miner creates a block B which contains address α, on which he wants to receive his rewards. An attacker changes block B, such that instead of α it defines a new address α’, which is controlled by the attacker. Will the attacker receive the rewards that the miner tries to claim and why (or why not)?

My idea was that first of all the attacker would have to redo the proof-of-work. Therefore it is unlikely that their blockchain would be the longest. However, is there any way that the attack could go through other than solving the proof-of-work faster than the rest of miners? What if the attacker changes the most recent block? Could the block then be on the longest chain?

I have also read that the Block Reward in a stale block is no longer spendable on the difficultywise-longest and well-formed blockchain; therefore whoever mined that block does not actually get the reward (or the transaction fees). So if the attacker’s changed block becomes a stale block, does this mean the reward cannot be claimed by the original miner or the attacker?