Few days ago I found on a website that my professor's student won the "Golden Kingfisher Prize" for her presentation under his supervision in his previous university 2 years ago .. Do you think it is good to talk about it? And what is the best way for this ?.
Professors are people too, hence any acknowledgement of achievements and, as in this case, their part in an achievement is always a nice thing to do.
It would probably not be a good idea to make too much of a big deal of it - but an email or a chat of congratulations to your professor is a polite acknowledgement and appreciation of a significant achievement.
Most of all, know that you are working with an academic that has, in some way, facilitated a student earning a great award. Just keep that in mind in all your future interactions with the Professor.
If I were you, I would approach them privately (this dismisses all possible concerns the Professor could reasonably have of brown-nosing/self-interest). The caveat is that you need to enter the conversation gracefully - I don't assume you would be congratulating the Professor out of anything but your own kindness and gratitude to said Professor, but a rekindling of communication after a number of years always sets up a warning flag among the weary.
If you had a strong relationship with the Professor, I'd recommend simply talking to them about it - asking what they learned from the experience, what advice they would give to you in areas relevant to this field, how they learned to adapt to the learning styles of others, etc. Put more simply, make it clear that you're interested and still eager for their insight on things, but make sure you personalize it to them - after all, it was their achievement.