Sorry late answer. Has been very busy.
Checked yesterday. Lifted up the atv, all four wheels up from ground.
When driving, only one wheel was turning around. When holding one wheel with my foot, the other wheel started turning.
When giving hard throttle both wheels start turning same direction, but only in the start of giving throttle.
Is it possible that the limited slip is a little bit "lazy" and/or is it possible to adjust the diff to engage earlier??

 

Why not do the test I indicated? " The best test is to lift both front wheels off the ground, with the machine stopped and rear brake on, and turn one wheel by hand. With limited slip, you should feel a resistance to turning but if you push hard enough it should start to turn, while the other front wheel revolves the opposite way."

I don't know if you can adjust it, the parts list shows it as a unit, so you can't get new clutch plates or springs separately.

 

I am so sorry!
I forgot to write that!
Yes. I took the test you indicated, but I didn`t feel a resistance while turning, rather I felt it was quite easy to turn. But when I pushed harder the other wheel started to turn the oposite way.

 

Another way to tell your in diff lock is the front is almost un steerable , that's why many ATVs will not engage diff lock unless its in low range or has a speed limiter.
Diff lock is only used for short periods or a few feet to get you out of a spot that normal 4wd (3x4) can not.

30mph while in diff lock would be suicidal. LOL

 

If there was no resistance to turning your limited slip mechanism is not working. I'm not certain how Yamaha's system worked, but on Hondas it is just a set of clutch plates with a spring keeping them together, when the strain of one wheel going faster than the other, in a turn, gets too much, the plates slip against one another, hence limited slip. Quaife style diffs in cars allow the wheels to move like a normal diff until the speed difference is too great, then they lock, but I doubt if Yam use this type.