It's true that Islam is a Christian heresy but to be fair, Islam tries to be it's own State Religion only for the Arabs. So in that sense it's not the same God since they don't believe in the Trinity.
Fun fact - not every Christian sect believes in the trinity.
Another fun fact, the Jewish God and the Christian God are the same… it’s just that the Jewish God didn’t have a son who was also himself that killed himself only to resurrect himself negating the sacrifice
Incorrect translation, Allahu Akbar means “the god is the greatest”
Allah is not a name that came with Islam but existed before, it just means deity. the Al prefix is the definite singular form. It just says one thing: god is a singleton and nothing is above it.
When Indian army regiments, with predominantly Sikh soldiers, fight any army, they rally themselves for battle with cries of "Wahe Guru ki Khalsa, Wahe Guru ki Fatah" (which roughly translates to "[We] the pure are of the almighty, and the triumph in making is also of the almighty). Pakistani army, predominantly Muslim soldiers, do use the rallying cry of "Allahu Akbar". It's debatable whether these chants are meant more for themselves, than directed at their "enemies".
It's true that Islam is a Christian heresy but to be fair, Islam tries to be it's own State Religion only for the Arabs. So in that sense it's not the same God since they don't believe in the Trinity.