Is “After the great victory over the Wei army at the Battle of Maling, did the Qi general Tian Ji force Zou Ji to retreat and become prime minister?” true?

The Records of the Grand Historian, in the biography of Sun Tzu and Wu Qi, records the historical facts that Tian Ji, as a famous general of Qi, with the assistance of Sun Bin, won through horse racing and led troops to great victories over the Wei army at the battles of Guiling and Maling. However, afterwards, Tian Ji was framed by Cheng Hou Zou Ji and once fled to the state of Chu. Although he was recalled and restored to his former position during the reign of King Xuan of Qi, historical records do not mention his appointment as prime minister. In Chapter 89 of the Chronicles of the Eastern Zhou Kingdoms, for the sake of a 'happy reunion' and satisfying revenge narrative, it is fictionalized that Zou Ji, 'thinking of his past private acceptance of bribes from Wei and his attempt to frame Tian Ji, felt guilty, so he claimed to be seriously ill and sent someone to return the prime minister's seal. King Xuan of Qi then appointed Tian Ji as prime minister,' a perfect ending.