Charging phone battery from DC supply
Charging lithium batteries is handled by the charging circuit found inside your phone , this circuit handles undervoltage and overvoltage protection of the lithium battery for safety concerns and battery life.

The charger you plug into the wall ( AC mains ) contains mainly a transofrmer and rectifing diodes. 

So simply plug 5v into the phone is safe and no need for any circuit. you can just use usb connector and connect only the power pins leave everythng unconnected and you are good to go.