Is “Did Cheng Yu forge a letter from Xu Shu's mother to trick Xu Shu into joining Cao Cao, and did he see through Huang Gai's false surrender?” true?

In the novel, Cheng Yu is resourceful and decisive, and is a key figure in tricking Xu Shu and seeing through the chain-link scheme. For example, in Chapter 36 of Romance of the Three Kingdoms: "Cheng Yu obtained Xu's mother's handwriting, then imitated her calligraphy, forged a family letter... and tricked Xu Shu into coming here." In Chapter 49, he also sees through Huang Gai's false surrender: "Cheng Yu observed for a long time, then said to Cao Cao: 'The incoming boats must be deceptive. Do not let them approach the camp.'" However, in Records of the Three Kingdoms, Book of Wei, Biographies of Cheng, Guo, Dong, Liu, Jiang, and Liu, his main achievements are recorded as "defending Juancheng and the two counties of Fan and Dong'a" and military strategies. The official history does not record that he forged a letter from Xu's mother, nor does it mention that he saw through Huang Gai's false surrender or the weakness of the chain-linked ships to fire attack.