[SunkenCiv]

The idea that the Khazars converted is a recent invention, and there's absolutely no basis in fact for it. It has been used as an excuse (by its inventors, among many others) to claim that the Hebrews of the Bible are actually ancestors to this or that European nation, rather than to modern Jews. It's yet another (and somewhat cryptic) form of anti-Semitism. This isn't to say that there hasn't been intermarriage during the 27 centuries since the Assyrians dispersed ten of the tribes. But they wound up in unexpected places, at the fringes of the Assyrian-ruled areas, including Central Asia and the Crimea.

• The Edicts of King Ashoka
• Are the Taliban Descended From One of Ten Lost Tribes of Israel?

[achilles2000]

“It’s yet another (and somewhat cryptic) form of anti-Semitism.”

While the theory may or may not be wrong, the prime exponent in recent memory was Arthur Koestler. I don’t think that there is any anti-semitism involved even if it is wrong (and I hold no position about the theory, but did think Koestler’s book was interesting). Do the Anglo-Israel people use this as part of their claim that the original inhabitants of Britain(or some group of inhabitants of early Britain) were Hebrew? BTW, regarding your point about the lost tribes ending up on the fringes of the Assyrian Empire, the 10th or 11th Edition of the Encyclopaedia Britannica (about 1910), I believe, had some interesting material chronicling Jewish traditions in at least one Afgan tribe.