How long is the moon full Is the moon the most full only for one moment 

As stated  here and here

Or does if stay the same full for a longer period of time (maybe because, the sun is grater then it, and light spreads out)

Full Moon Position of Sun
tl;dr: Perfectly full moon lasts, never more than, approximately 2 minutes.

Estimating an answer from the point of view of Plain Geometry:

If we approximate, that the sun is at an infinite distance, then exactly half of the moon is illuminated.

Next, how much of the Moon do I see when I look at it from Earth? (This has nothing to do with illumination of the Moon.) Estimate: Radius of moon (Rm), 1740km. Distance to the moon (Dm), 384,000km. Doodle this into a diagram that is VERY much not to scale...



arctan(Rm / Dm) gives us 0.260 degrees. So as long as the observer is within that angle from the Moon-Sun-centerline, the portion of the Moon which is visible, would be a circular disc fully illuminated.

Here, I suspect that the variation in the Moon's distance is the biggest thing I've estimated away.

The question now is: combining the Moon's motion of revolution (aka orbit about the Earth) with the Earth's rotation, how long does it take an observer to perceive the moon moving half a degree (1/4 degree either side of the Moon-Sun-centerline)? Rotation of the Earth gives 15 degrees-per-hour, minus the Moon's 1/2 degree per hour... 14.5 degrees per hour apparent motion.

I get approximately 2 minutes duration when the Moon's shifting of apparent position would only hide/show illuminated portions of it's disc.

But the lunar orbit is inclined

So it's only 2 minutes if the Moon is very close to the plane of the Equator. As the Moon's orbit carries it out of the plane, the time would be reduced. Beyond half a degree out of the plane, you would actually never (pure geometry) seen a fully illuminated disc.

So I think the best answer is probably, "Never more than 2 minutes."