A search for keywords Hungary genealogy on Google Blog Search brought up an interesting blog item. Apparently written by a member of LDS this article gives some insights into how Mormons found the way to the Soviet block: The Iron Curtain: Thomas S. Monson Helped Pull It Down. Extract:
"One of the most effective of the Lords ambassadors was the Churchs microfilming work. In 1957, Hungary approached the Genealogical Department (now the Family History Department) regarding the preservation of its records."