Armenia was the first country in the whole world to adopt Christianity as the state religion. Armenians have a "quarter" in Jerusalem, and were key guardians of Christian sites and relics there for several centuries when few other Christians were left in the city. It would not be surprising at all for them to have a relic of this kind. The country is over 98% Christian, that's one of the highest percentages in the world.
But this is not Armenia -- this is Bishkek.