Recentish research has shown this story to be wrong.
For a while the best evidence in its favour were a couple of interviews given in the mid-Nineties by the late John Lansdale suggesting that this had been the fate of the uranium from the U-234. However, while Lansdale was a senior figure in the Manhattan project, there were always those of us who wondered why his particular responsibilty - security - would have given him knowledge of the matter. Other members of the project who were closer to the details of the production chains had denied the story.
I’ve recommended Joseph Scalia’s Germany’s Last Mission to Japan (Naval Institute Press, 2000) on the Dope often enough, but it did have the weakness that, as a naval historian, he wasn’t that interested in the uranium and thus pursuing the trail into the Manhattan Engineering District paperwork. He did establish that the uranium was still sitting in a warehouse on July 2nd.
At that point it seemed unlikely, given that there were only three weeks available, that any of it wound up contributing towards the weapons used against Japan. The production chains were far more complicated than even detailed popular histories convey, with the raw material having to be processed through multiple plants, involving trips back and forth across the US, before uranium got anywhere near either Hanford or Oak Ridge. Even if they had started using the U-234 uranium immediately, there just didn’t seem to be enough time.
That argument became irrelevant once Robert Norris, General Groves’s biographer, turned up good documentary evidence that the uranium hadn’t been used. As he described here. (Incidentally, this is the only occasion I’ve seen a - minor - historical mystery being resolved by an archival discovery announced in an Amazon customer review.)
It’d be entirely unsurprising if some seized German uranium did wind up contributing to the 1945 bombs - plenty of it was captured in France, Belgium and Germany in 1944-5. But the stuff bound for Japan on the U-234 didn’t.