This question already has an answer here:
When miner creates a valid block he broadcasts that to the network.
It can happen that someone else did the same. So we have half nodes think that chain+A is correct, and other half that it is chain+B. This gets resolved when next block is solved.
When are the coins given to the miner, or are they given to both miners?
How do the coins get sent to the miner?
Does the solved block contain the identity (public address) of the solver so the protocol can send him money? https://en.bitcoin.it/wiki/Block_hashing_algorithm - can't find that address here
EDIT: Now it seems to me that both are rewarded, each inside his respective fork. Something like the reward transaction is put inside that chain-head. When one fork wins the respective reward stays as valid and the other fork is dropped by community. Am I correct?