Very good.Well, the dates you mention don't actually add up. The Jew (individual) who is described as arriving in Poland in 965 or 966--which coincidentally around the same time that Khazaria was being destroyed by the Rus'--was a Sephardi Jew with an Arabic name who was traveling along the Silk Road from Andalusia. In other words, there's zero connection between the two.
Mention of the first permanent Jewish community in Poland doesn't occur until over 100 years later, and it's mentioned by a German Jew, likely due to connections between the two communities. For hundreds of years after this, we know of numerous waves of migrations of Jews from Central/Western Europe into Poland, which gradually builds up the Jewish population in Poland.
Whatever Khazar Jews who were not extensively mixed with Persian and Greek (Anatolian or Balkan) Jews, likely converted to Islam or Christianity. Because, again I can't stress this enough, there's no genetic evidence of any significant (as in even a single percent) Khazar ancestry in modern Ashkenazi Jews or Mountain (Caucasus) or Georgian Jews. So even if there was an historical connection between the two, which there isn't, the genetic evidence would still refute it.
Again, if you're genuinely interested in the subject, check out khazaria.com. It can be tough to navigate because the interface is outdated, but there's tons of valuable information about both the Khazars and the relevant Jewish communities.
Well I have to thank you for actually giving relevant information on this debate rather than a couple of other posters I could name who feel the innate need to go on the attack about Anti-Jewish agenda BS on anyone that queries the theory, they could learn a lot from you.
Factual information are the tools to win a debate not baseless or reactionary accusations, so again thanks for giving me actual valuable information on this subject, I'll look into it but if what you say stands up then it puts to bed that theory.