Allah, as the Muslim undertand him, is the object of their faith. The Muslims did not make their faith from whole cloth by from bits and pieces of Judaism and CXhristianity. The early Christians thought it a Christian heresy, a newer version of the heresy of Arius.
True, though in the first 100 years or so of Christianity, the Jews at the time didn't think of Christians as a new religion, but rather as a Jewish Heresy, and a bunch of renegade Jews causing problems in the temples by worshiping a false messiah. It wasn't until later that Christianity was seen as a distinct, separate religion.