You can actually use a heat gun.
Clamp the connector to the board where it is supposed to go. Use a magnifying glass to make sure it is perfect. Then heat it up with the heat gun while watching it under the magnifying glass. You will see the solder melt to the connector. You are done
Or you can buy a real fine solder tip. Just clamp the connector as described and touch each pin for a second and it will re-attach to the board. Use a magnifying glass to work.