Direct Narration :
She said to me, " I was teaching this lesson on his request."
Indirect Narration :
She told me that she had been teaching that lesson on his request.
Conversion is ok but what about the time factor which is said to be compulsory in a sentence pertaining to perfect continuous tense ?
If I try to add a time factor with since or for, it would be a false statement because the time factor has not been mentioned in the original sentence.