َQ:

Is it permissible to consume meat of game , if the shot fired but christian brother and i pray (say Allah name) on behalf of him?

A:

Allah says in the Quran, “Today I have permitted for you all the good things and the food of the people of the Book are lawful for you and your food is lawful for them.”

According to Ibn Abbas, the above verse refers to the meat slaughtered by them; this also applies to the game they have caught. 

This is the view of most scholars ( of the four schools, including Hanafi, Maliki, Shafi, and Hanbali). That’s also has been the position of Ata, ath-Thawri, al-Awzai, and others as well. 

According to them, game catching by using dogs or firing shots is analogous to slaughtering.

In conclusion, you are allowed to eat the games caught by the people of the book.

Almighty Allah knows best.