Aim, I think you have some historical facts a little distorted, Eastern Jerusalem (the walled city) was conquered by Jordan (and the Jewish quarters sacked, and the four Kibutzes in Gush Etzion conquered as well), the rest of Jerusalem, the Israeli managed to defend despite a siege (and no water) that lasted a good six months. When I got to Jerusalem it was still under siege, and I remember vividly the water rationing. The orphanage, where I was "dumped", had a cistern, and once a week a truck would deliver water, and I remember standing by the pipes capturing some of the leaking water....In 1967, Israel conquered the whole west bank including the walled city. The big concrete walls and barbed wires between the two cities were eradicated and the city was reunified. During all that time, Jerusalem (Western Jerusalem, if you wish) was the capital of Israel, even though, the US did not recognize that fact. By the way, the US did not back Israel for a long time, only after 1967 did the relationship between the two countries warm up. The 1948 conflict was won with supply of arms from the eastern block (through Chehoslovakia), from 1953 on France was the major supplier of advanced weapons, and only in the late 60' finally did the US/Israel relationships warmed up.
By the way, I have a degree from the Hebrew University, which is in the capital, Jerusalem, and won that degree long before 1967 (by then I was already in Columbus OH <g>)