Why does the heater works while sitting still but it blows cold air when the vehicle is moving?

You could have a problem with a failed thermostat. It may be stuck open and when air is not being blown thorugh at higher speeds the coolant gets colder than it is supposed to. Normally the thermostat would close when so much air is making the coolant drop below the specified temperautre by shutting the flow of coolant down for a moment until it has warmed up to operating temperature. This cycle keeps the engine coolant at the specified temperature which would keep the heater hot.
Try replacing the thermostat and see if that does the trick.

Check thje heater core valve. It is on one of the hoses that run from the engine to the heater core through the firewall. It will be near the firewall and cave a cable running to it. This might be stuck or the cable is not held in place properly. Check to see if it moves frmo fully opened to fully closed when turning the heat up in the car.