Cizinec,
I am told - I do not speak Arabic - that the word 'Allah' is the Arabic word for God. If we accept that and move on to a comparison between the New Testament and Al Qu'ran we may find an answer.........
THE KORAN
The similitude of Jesus before God is as that of Adam; He created him from dust, then said to him: "Be"; And he was. (Sura 3, 59)
THE NEW TESTAMENT
In the beinning was the Word, and the Word was with God, and the Word was God. The same was in the beginning with God, All things were made by Him; and without Him was not anything made that was made..... And the Word became flesh, and dwelt among us, (and we beheld His glory, the glory as of the Only-begotten of the Father), full of grace and truth. (John 1, 1-3, 14)
THE KORAN
They do blaspheme who say: "God is Christ the son of Mary..." They do blaspheme who say: God is one of three in a Trinity, for there is no god except One God. If they desist not from their word (of blasphemy), verily a grievous penalty will befall the blasphemers among them. (Sura 5, 75 & 78)
THE NEW TESTAMENT
All power is given Me in Heaven and on earth. Go ye therefore, and teach all nations, baptizing them in the Name of the Father, and of the Son, and of the Holy Spirit: taching them to observe all things whatsoever I have commanded you: and lo, I am with you always, even unto the end of time. Amen. (Matthew 28, 18-20)
No one, reading the texts given above could in reason conclude that the 'God' moslems worship and God that we worship are one and the same.