According to this website, there are a number of biographies of Shankaracharya called shankara vijaya.
The oldest among them is the Madhaviya Shankara Vijaya, by Vidyaranya
mAdhavIya Sankaravijaya - The mAdhavIya is probably the oldest available, and also the most authentic and widely known among the different Sankaravijayas today. It is certainly the most popular such text in the advaita tradition, and is also known as the sam.kshepa Sankarajaya. The popularity of this work derives from the fame of its author, mAdhava, who is usually identified with vidyAraNya, the 14th century maThAdhipati at Sringeri.
So it's possible that this would be held as the most original source of this account.
The book 'SRI SHANKARA DIGVIJAYAM, AN CONCISE ENGLISH TRANSLATION ADAPTED FROM
SRI MADHAVIYA SHANKARA DIGVIJAYAM BY SRI VIDYARANYA' is available online and it is a english translation 'adapted' from the same book. I am not sure what they mean by 'adapted from sri madhaviya shankara digvijayam' but there you go.
Here is how it describes the account of the debate:
Mandana, however, still had some questions regarding the aphorisms of Jaimini and their
relation to the Absolute Truth, as propounded by Sri Shankara. When Sri Shankara clarified, Mandana prostrated and said, ‘You are the nature of pure consciousness, yet for the sake of ignorant men you have assumed this human body. You have saved all with the single statement - Tat tvam asi, and explained the great soul indicated in the Upanishads, the crest-jewel of the Vedas, as indestructible and one without a second.’ Praising thus, Mandana then surrendered himself at the feet of Sri Shankara
This story is famous by all advaitins and most of the Advaita saints have narrated this story when describes Shankaracharya's life History. The moral is mostly about how debates in the olden days were done in good spirits and not with any ego. Sometimes it is about the moral values of Mandana Mishra's wife Udhaya Bharati, which is a story by itself. All the best!!