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However it seems to be that I loose time and elasticity and when I have to switch from 9-11-12 to 9-11-13 because you have to reposition the pinky. However if I try to play the 9-11-12 parts with index, middle and ring finger I find it a very uncomfortable stretch.
It looks to me from the video (which due to the clarity of the sound makes it almost impossible to determine the nuances of the run) that your pinky is hitting the 12 and 13 fret at random. Either way, that kind of shift of whole-half to whole-whole intervals is a very common and frequent happence in scales, so it really is something you got to practice until your fingers don't even notice it.
Also, if you find that kind of stretch uncomfortable for 3 fingers, you should try getting into 3 notes per string diminished string skipping stuff.

It really works your fingers to the bone, particularly once you get below the 11th fret. After you get used to it it isn't as hard as it sounds (Unless you're playing it at the speed rusty cooley or gus g do them, but that doesn't count).
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What would be the best approach to this ? And how difficult do you classify this kind of run ? My biggest problem is to play up to tempo and in synch... anyway here goes

I'd say this is a pretty simple and easy run, considering the position shift isn't that hard to get used to, there's no odd patterns that you have to slow down until your fingers get used to (barring the ending thing with the bend but you can easily noodle around there for a second and it will more or less sound the same), no string skipping, the beats line up easily, etc. The only 'hard' part is the actual speed that you are playing it at.
Practice your scales, eat your greens, etc. Considering the problem lies only with speed simply proves you have to work some more so you can play more fluidly at higher speeds.
Personally, I could more or less get the whole run down (except for the ending) and up to speed, using the same fingers you use, in about a minute. As I said, it's a fairly simple ascending run thingy. ;P
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However, from the symmetrical looks of the scale, I'd suggest that the 13th fret note should have been a 12th fret note anyway. :-)
That would cause you to play an outside scale note; the minor 2nd of the scale, when you just played the major 2nd, which is kind of silly. And 'faking' your way through by playing shapes rather than real scales isn't a sound idea (pun intended).