Is “Regarding the matter of Emperor Shenzong sending Teng Fu to convey an imperial edict to comfort Yang Hui, it is recorded in detail in Yang Hui's biography, but it is not mentioned in Teng Fu's own biography.” true?

The 'History of Song: Biographies of He Chang, Wu Zhongfu, Ze Ren, Chen Jian, Wang Lie, Sun Sichong, Zhou Mengyang, Qi Hui, Yang Hui, Liu Xiang, Zhu Jing' records in detail that when Emperor Shenzong demoted Yang Hui because he offended the prime minister, he specially ordered Teng Fu to convey his true intentions to Yang Hui to comfort him: 'The emperor ordered Fu: "... Just let him avoid for a while, you should convey my intention to him."' However, as the key figure who conveyed the edict, Teng Fu's own biography in the 'History of Song: Biographies of Teng Yuanfa, Li Shizhong, Lu Shen, Shi Min, Zhao Xie, Sun Lu, You Shixiong, Mu Yan' makes no mention of this incident of conveying the edict, which reflected the emperor's trust.