The velocity of the Moon is obviously about the same as the Earth because it orbits at about the same distance. If you set the Moon's initial velocity to it's orbital velocity relative to the Earth (NB 1.022km/sec not 1.022m/sec as you state) then it will just fall towards the Sun, as indeed you've found.

You say:

I tested also to start the simulation with the velocity of moon = 29.783 + 0.001022 , (earth velocity) but then the moon just turn around the sun like the earth

Well you would expect the Moon to orbit the Sun just like the Earth. The orbit of the Moon looks extremely similar to the Earth because the distance from the Earth to the Moon is just 0.25% of the distance from the Earth to the Sun.

The velocity of the Moon is obviously about the same as the Earth because it orbits at about the same distance. If you set the Moon's initial velocity to it's orbital velocity relative to the Earth (NB 1.022km/sec not 1.022m/sec as you state) then it will just fall towards the Sun, as indeed you've found.

You say:

I tested also to start the simulation with the velocity of moon = 29.783 + 0.001022 , (earth velocity) but then the moon just turn around the sun like the earth

Well you would expect the Moon to orbit the Sun just like the Earth. The orbit of the Moon looks extremely similar to the Earth because the distance from the Earth to the Moon is just 0.25% of the distance from the Earth to the Sun. The movement around the Earth is a small perturbation of the orbit round the Sun.