It is likely that the Eckert-Mauchly team had arrived earlier at this idea, but there is no evidence about this.
Despite the possible precedence of Eckert, von Neumann is the one who deserves full credit for the content of the report, including the "von Neumann Architecture".
The decision made by von Neumann to distribute this report has provided incalculable benefits for all mankind. The report described how to make an electronic computer in a much more clear way than any of the Eckert-Mauchly team would have ever been able to explain.
The effect of the von Neumann report has been that multiple teams, first in USA and UK, then also in many other countries, have started immediately to work at the development of electronic computers, leading to a large number of successful research projects then to an explosion of the computer industry.
The public distribution of the von Neumann report has annoyed a lot the Eckert-Mauchly team, who wanted to keep these developments secret, because they were preparing the creation of their own startup company, in order to exploit computer technology for becoming rich. Without the interference of von Neumann, the creation of a big computer industry could have been delayed by a decade and it certainly would have been much less diverse.
After the war, the Eckert-Mauchly team has never made any significant technological progress, all the essential inventions that have improved the electronic computers have been made at a great number of companies, research institutions or universities. Had the design of electronic computers remained a monopoly, that would have happened much later.
Moreover, the Eckert-Mauchly team did not have much grounds to consider themselves as the owners of electronic computer technology, because they could not have done anything without a great amount of money from the government, and at the beginning they have also taken useful information about the electronic computing circuits used in the Atanasoff-Berry computer, without later acknowledging any of their sources of inspiration.
It will never be known how much of the von Neumann report has been created by von Neumann and how much he had already learned from discussions with members of the Eckert-Mauchly team. However, this does not matter, because either way the von Neumann report is what has taught the world how to make electronic computers.
