Of course Booker T. Washington was to some extent a politician, who existed in a world controlled by others.
He needed to make at least some peace with the southern whites, and gave at least lip service to Lee/Jackson as a way of reducing support for racist murderers from otherwise decent people of the south.
Any other evidence that Lee taught a black Sunday school? I have heard that Jackson had, but in no way was he the first.
A church in Savannah, First African Baptist, was running a Sunday School in 1826