There is a man who has memorised the Bible. He calls Christians to Islam and even debates them using their own books. Is this permissible?

Shaykh Muqbil ibn Hādi al-Wādiʿī:

It has been related in Ṣaḥīḥ al-Bukhārī that the Prophet ﷺ said: “Do not believe [news from] the people of the book nor reject them. For you may either believe in falsehood or you may reject the truth.” And seemingly, the additional [wording] “For you may either believe in falsehood or you may reject the truth” is not in Ṣaḥīḥ al-Bukhārī. Ibn ʿAbbās said: “Your Book is the most recent [revelation] from your Lord. Have you seen anyone from the people of the book ask you?” The point is [the people in question] are not upon the correct path. Allah said:

۞ فَبِأَيِّ حَدِيثٍ بَعْدَ اللَّهِ وَآيَاتِهِ يُؤْمِنُونَ

Then in what speech after Allah and His verses will they believe?
” (Q 45:6)

And when the non-Muslim from Quraysh would come to the Prophet ﷺ, he would recite the Qurʾān to them. So much so that Jubayr bin Mutʿim came to the Prophet ﷺ whilst he was reciting praying Maghrib and reciting Sūrah al-Ṭūr. And [he recited] until he reached the statement of Allah ﷻ:

 ۞ أَمْ خُلِقُوا مِنْ غَيْرِ شَيْءٍ أَمْ هُمُ الْخَالِقُونَ

Were they created by nothing, or were they themselves the creators?
” [Q 52:35]

Jubayr said – and [at that time] he wasn’t a Muslim – “My heart wanted to fly from my body out of awe.” In another narration he said: “It was then that belief entered into my heart“. So I advise you to call the people to Islam using the Book of Allah and the Sunnah of the Messenger.