I assume that it moves onto the laptop display when the graphics card drivers fully load, prior to that it shows on the external monitor ?
If so then there should be a setting in the display properties to allow you to select either display as the primary and also a clone option so that the display is sent to both.
If you look in the device manager it should tell you which graphics card you are using or if its an onboard one and if you let us know which one it is then we may be able to find the correct procedure for you