The Theravada school had also reached Burma around the time it arrived in Sri Lanka and something of a synergy gradually developed. Around the end of the 10th century, for example, war in Sri Lanka had extinguished the Theravadan ordination lineage, and a contingent of Burmese monks had to be imported to rekindle it. Burmese and Sri Lankan Theravada reinforced each other sufficiently, so that by the time Buddhism died out in India in the 11th century, it had established a stable home in these countries.
http://en.wikipedia.org/wiki/Theravada# ... _tradition
It seems to me that this claim is overrated. I feel it is difficult to find documents about early buddhism in Burma. The first documents relate what happened during 11th century. Is it that sinhalese chronicles support this statement about relations between Sri Lanka and Burma?