Disagree.
The "god" of the old testament was a god entirely and solely for the Hebrews. That god would never, ever have branched out to non-Hebrews (even closely-related ones like Arabs), and promised to send a messiah (which was entirely an *earthly* king and savior, not a "spiritual" one as the christians claim).
The "god" (Allah) of the Muslims is not a god entirely and solely for the Hebrews, so it's not the same god. The "god" of the christians didn't send an earthly messiah, and branched out to the gentiles, something the OT Hebrew god would never do.
They are three different concepts of a "god." With different rules, goals, promises, "tribes," etc.
Peace.