Who issues the transaction of reward when a miner solves the block?
The miner itself includes a special transaction in the block called generation transaction. Every block only has a single generation transaction. 

This generation transaction transfers the block subsidy plus the fees of the block to an address controlled by the miner.

For intance, if you look at block 434868, there is a single generation transaction that transfers 12.96 to address 17ggdTQzKFwrKP1zgqb5Kjuw6CpGKaE6Jrw.