Start with an element of basic Christian theology: G-d as universal, the Creator of all things. We know (and can prove) that by its very Nature language does not and cannot encompass the universal (Gödel's proof). Therefore, as Paul (1 Corinthians 13:12) says:
...now we see in a mirror, dimly, but then we will see face to face. Now I know only in part; then I will know fully, even as I have been fully known.It therefore follows that if we pray to G-d simply as we conceive G-d to be, we necessarily pray to an incomplete idea of G-d. As C. S. Lewis put it, we must, logically, pray to G-d as G-d knows G-d's self to be. If we do this in humility, acknowledging our inadequacy to fully conceive of G-d but directing our worship to the great "I am" (Exodus 3:14), and if Muslims do the same, then they and we necessarily pray to the same G-d. And if we do not, if we pray to our conception of G-d, then we can only hope in humility for G-d to bridge the inevitable gap between the limited concepts in our minds and the transcendent reality. And if Muslims do the same, do we dare ask that G-d not grant them the same mercy?