Ancient Chinese officials are known to be divided into two categories: The Wen officials (officials handling civil matters) and Wu officials (generals/martial officials handling war-related matters). However, when did this classification start? Was this always rigorously enforced, as in no individual could switch to being a civil and war official at any given time. Moreover, as the question stated, has there been examples whereby a civil official became a war general or a war general becoming a civil official?
While I can't comment on when exactly did this distinction start, I can provide an example of the "switching".
Ban Chao from the Eastern Han Dynasty, started out as an copyist and was also appointed as Clerk of the Prefect of the Orchid Terrace (蘭臺令史), an official in charged of documents and book in the imperial court . Very much a 'wen' civil official. But Ban Chao later went on to lead Eastern Han armies in various battles in the Western Realms (西域). Some of the military titles he held include Assistant Commander (假司馬) and Division Commander (軍司馬). He was also given the title of Marquis who pacify the faraway lands (定遠侯) for his feats.
This transition is recorded and well-known due to Ban Chao's own explicit desire to 'switch'.
永平五年，兄固被召詣校書郎，超與母隨至洛陽。家貧，常為官傭書以供養。久勞苦，嘗輟業投筆歎曰：「大丈夫無它志略，猶當效傅介子、張騫立功異域，以取封侯，安能久事筆研閒乎？」左右皆笑之。超曰：「小子安知壯士志哉！」
In year 62 AD, [Ban Chao's elder brother] Ban Gu was appointed as an editor in charged of processing documents. Ban Chao and his mother also followed him to Luoyang. His family was poor, and Ban Chao worked as a copyist for the government to support the family. It was tiring and he would often threw his writing brush down and sigh, "Real man with no exceptional ambitions and strategies should at least be like Fu Jiezi or Zhang Qian, achieving great accomplishments in faraway lands, gaining nobility titles. How could they be handling brushes, ink, paper and inkstone all the time?" Those beside him would all laughed at him when they hear this. Ban Chao then said, "How can ordinary people understand the goals of people with lofty ideals?"
This eventually evolved into a Chinese chengyu, or idiom, 棄筆從戎 -- referring to one giving up civilian (especially academic/literature) pursuits to join the army in a positive light, such as to defend one's country etc.
Biography of Ban Chao, Book of the Later Han
A dictionary of official titles in Imperial China, Hucker