In Morrowind this was often the end of the lesson, but I have seen it in Skyrim now as well in the book http://www.uesp.net/wiki/Skyrim:Sithis
I do not really care about Sithis in and of itself but I do care that so many 'fingerpoints' say 'Go to the Sharmat as a friend' I know it is not the only time it is written.
I don't recall seeing the phrase "Go to the Sharmat as a friend" anywhere else, but I could be wrong. If you could show me another place it's written I'll look at it.
Based on the context, I'd say it means "gain his trust in order to betray him."