“Check your Arabic Bible and you will see that Allah is the Arabic word for God.”
I will defer to your experience on the subject, but I remain unconvinced that Muslims believe their god is the same entity as the God of Abraham, Isaac, and Jacob.
Of course the Muslims totally distort Biblical truth, and thus are promulgating rank heresy. They have twisted the truth about God (as discussed, Allah in Arabic) for their own evil purposes. That does not change the fact that Arab Christians use Allah as God, as it appears countless times in the Arabic translation of the Bible (which predates the English translation of the Bible by centuries, by the way)
Muslims certainly believe that, and say it quite loudly and often. Their take is that the Bible is corrupted, and Abraham, Isaac, and Jacob were all good proto-Muslims.
Whether that's the truth is a different question.