Air conditioner compressor toggles on and off too soon

Replaced the air conditioner compressor. Air conditioner repair put in right amount of gas, replaced a leaking valve, but the air condition does not cools properly. The air condition repair center says that is because the compressor toggles on and off too soon, and does not give the compressor a chance to work enough to cool the air.

They told me that I should go to the Ford dealership and let them put it on the computer and that supposedly they could make the compressor stay longer before it switches or toggle on and off.
So I go to the dealer and ask them before paying to put the computer on the car if that is through if the computer can do that, and they tell me no. So they could not tell either what it is. So now I turn to you to see what could be wrong that the compressor switches on and off too soon while the gas, pressure everything else is working fine.

Thank you very much and I hope to hear from you soon!