If One of the People of the Scripture Slaughters an Animal and He Does not Mention Allah's Name Over it

Question :

If one of the People of the Scripture slaughtered a sheep as a Muslim does, but he did not mention Allah's Name over it, because they believe in the trinity, is it permissible to eat this slaughtered animal?

Answer:

If one of the People of the Scripture slaughters an animal and we know that he mentioned Allah's Name over it, then it is permissible to eat it, because it is included in the generality of Allah's Words:
"The food (slaughtered cattle, eatable animals) of the people of the Scripture (Jews and Christians) is lawful to you.

But if we know that he uttered the name of other than Allah, then it is not permissible to eat it, because that is included in the generality of the Words of Allah, Most High:
"Eat not (O believers) of that (meat) on which Allah's Name has not been pronounced (at the time of the slaughtering of the animal) for sure it is Fisą (a sin and disobedience of Allah)."

If we are ignorant over whether he mentioned Allah's Name or left it, then it is permissible for us to eat from it. This is because the basic principle is that their slaughtered animals are permissible, according to the Words of Allah, Most High:
"The food (slaughtered cattle, eatable animals) of the people of the Scripture (Jews and Christians) is lawful to you."

Source:
The Permanent Committee
Fatawa Islamiyah, Vol. 6 Pages 317-318