The book you refer to is entitled The Islamic Invasion:
Confronting the World's Fastest Growing Religion, published by Harvest House Publishers, Oregon, US, 1992. The author, Dr. Robert Morey, sees Islam as an invasion into North America and a threat to his religious heritage.
Unfortunately, Dr. Morey has resorted to dishonest tactics in combating Islam. To prove his contention that Allah is not the God of Christians and Jews, he quoted from several books in such a dishonest fashion that the quotations say the opposite of what we find in those books (see quotations on pages 47-53 of Dr. Morey's book).
Dr. Morey quoted from the Encyclopedia Britannica to support his case. But in fact the Encyclopedia says:
Allah is the standard Arabic word for "God" and is used by Arab Christians as well as by Muslims (Britannica, 1990 Edition, vol.1, p.276).
Dr. Morey also quoted from H.A.R Gibb to support his case. But Gibb actually says the opposite. In his book Mohammedanism, Gibb says on page 26 that both Muhammad and his opponents believed in "the existence of a supreme God Allah." Gibb further explained this on pages 37-38 (see Mohammedanism by H.A.R. Gibb, Oxford University Press, 1969). Dr. Morey should have checked his references more carefully before his book went into print.
Dr. Morey said that Alfred Guillaume agrees with him, and he refers to page 7 of Alfred Guillaume's book entitled Islam. But here is what Alfred Guillaume actually says on page 7 of his book:
In Arabia Allah was known from Christian and Jewish sources as the one God, and there can be no doubt whatever that he was known to the pagan Arabs of Mecca as the supreme being (Islam by Alfred Guillaume, Penguin, 1956, p.7).
How could Dr. Morey misquote like this? Furthermore, Dr. Morey quoted from page 28 of a book by another non-Muslim writer Caesar Farah. But when we refer to that book we find that Dr. Morey gave only a partial quotation which leaves out the main discussion. The book actually says that the God who was called Il by the Babylonians and El by the Israelites was called ilah, al- ilah, and eventually Allah in Arabia (see Islam: beliefs and Observances, by Caesar Farah, Barron's Educational Series, 4th Edition, p.28). Farah says further on page 31 that before Islam the pagans had already believed that Allah is the supreme deity. Of course they had 360 idols, but, contrary to Dr. Morey's assertion, Allah was never one of the 360 idols. As Caesar Farah points out on page 56, the prophet Muhammad, on whom be peace, personally destroyed those idols.
Dr. Morey also quoted from William Montgomery Watt. But Watt says on page 26 of his book that the Arabic word Allah is similar to the Greek term ho theos which we know is the way God is referred to in the New Testament (see Muhammad; Prophet and Statesman by William Montgomery Watt, Oxford University Press, 1964, p.26).
Dr. Morey also quoted from Kenneth Cragg's book entitled The Call of the Minaret. However, on page 36 of Kenneth Cragg's book we find the following:
Since both Christian and Muslim faiths believe in One supreme sovereign Creator-God, they are obviously referring when they speak of Him, under whatever terms, to the same Being. (The Call of the Minaret by Kenneth Cragg, Oxford University Press, 1964, p. 36). Further on the same page, Cragg explains that the One whom the Muslims call Allah is the same One whom the Christians call 'the God and Father of our Lord Jesus Christ', although the two faiths understand Him differently.
Dr. Morey should know that as a scholar he has the academic obligation to quote honestly. He should also know that as a follower of Jesus, on whom be peace, he has an obligation to speak the truth.