This an example of of Li Changge's continous growth in intelligence even as the series progresses.
Concerning that secret letter from Li Changge to Li Si Min, mentioned in E39, I just wish to re-construct something that both HappyBirdEgg and myself wrote, in response to a question by Richaliya who asked how come Changge could do much without any positional authority. We wrote separately, yet came to pretty much the same conclusion.
Now, the drama has never shown us that letter. But we know from E39 that Changge wrote it. Shuyu ask her if that was the case, and she said yes. And that letter was written by Changge was read by Li Si Min (this was stated by Shuyu). How did Li Si Min know that it was from Changge? We felt that at that time, people could read the handwriting of others who are close to them. Li Si Min spent many good year with Li Changge. It would not suprise us that he could read Changge's handwriting and knew that this letter was indeed from her, even if it does not carry official seal of any kind (as Changge did not have any official position in Tang, once she left for the grasslands in E15).
And from an earlier episode, Du Ruhui had already reported to Li Si Min that Changge is alive and well. Hence, Li Si Min had no reason to believe that this letter did not come from her. Both Ru Hui and Li Si Min knew that Changge would never harm Tang, hence Li Si Min knew that Changge had good intention to form the peace alliance.
So Li Si Min sent Shuyu as the peace envoy to Mobei, to discuss the forming of the peace alliance, to counter the growing threats from Ashile Troops.
We both felt that this shows just how smart Li Changge was. She took a gamble and it paid off. She was willing to gamble that her uncle can read her handwriting, and that he would agree to her plan of forming the peace alliance. And his sending of Shuyu to Mobei was a confirmation of him giving her blessing to her plan.
We felt that this is the way the screenwriters wanted to portray Li Changge, that as the series progresses, Changge will get smarter and smarter. And her ability to come up with this complex scheme shows just how smart she has become.
All the three men in E39 - AS, Pusa and the King of Monan, were seated there with her. But none could up with a plan to counter YiCheng. It was Changge who did. She was so smart, even Pusa would later exclaim, I am so glad I am your friend, and not your enemy.
I just want to type this comment, in case it might be useful if someone asked just how smart was Li Changge, and who was it who conceived the peace alliane between Tang and the Desert tribes of Monan and Mobei. Not only did she conceive the plan, she will also execute it, going as Mobei Princess, along with the four others (Shuyu, Mimi, AS and the princess of Monan) to Chang'An, to negotiate peace with Li Si Min.