Modern Vespa

Hello
I have a problem, I only have around 9 volts to the headlight. I have 13 volts on the battery, can someone help me

The battery does not power the headlight. It's powered directly off the motor on your scooter. I would suspect lower voltages at idle, but when the motor is revved up, you should see 12-13 volts.

It was around 9 volts all the time

There's a stator plate that powers it and a regulator that regulates it from going above 12 volts. Either the regulator is working too well or the stator plate is not working well enough. You can measure the A/C voltage for the headlight going into the regulator to see if it's 13 or 9 volts. If it's 9, even when revved up, you would need a new stator plate.

... and remember to set your voltmeter to AC otherwise you will just be measuring offset or possibly half wave average.

It is not DC voltage?
And I have 14.5 volt to the battery when it was running in idle and a little bit more when I run the engine faster. Can I have a other problem maybe with the switch or something else.

It is not DC - it is regulated AC. You may find at idle it's below 12VAC, but when moving (over say 2000 rpm) you should see at least 12VAC.

The 9VDC you are measuring is the DC offset component of the AC.

OK thank you I gonna check that tomorrow

Can someone tell me the color code for the headlight
like ground, high and low
I have a H4 connector

From the wiring diagram ( http://manuals.wotmeworry.org.uk/Vespa/LX50/ - choose your model) it's:
Ma (Marron, Brown) for the dipped beam
Vi (Violet, Purple) for the high beam
Ne (Nero, Black) for the ground.

check at the hi/low selector switch, a poor connection or partially bad switch will cause voltage drop. Check for poor ground.

John