When it came to the content of the constitution, the Allies' conditions were clear and pretty general - it had to be democratic, and it had to be federal. (The latter was distinguished from the Weimar constitution only in that the Allies insisted on general size parity between states.) Plus complying with occupation policy on control of heavy industry. See https://de.m.wikipedia.org/wiki/Frankfurter_Dokumente
The main principles of the constitution itself were assembled by German elected governments of the states (https://de.wikipedia.org/wiki/Verfassungskonvent_auf_Herrenc...), and were very much direct responses to the process of the Nazi takeover in 1933.
Please don't forget that (1) the allies had really diametrically opposed goals -- France had to be coerced by the UK and the US to agree to the draft constiution. Moreover, (2) the allies tried hard to avoid the impression that they were forcing anything on the german drafters. Only the date for the drafting conference was an allied constraint: 1. September 1948. The allies wanted to West-German population to accept the constitution, remember the cold was was hotting up at the time, and Soviet union was good at exploiting discontent.
approved of the Germans
that went there