Those PC's came with a Recovery Partition. If that is still there, you can make a Recovery DVD set or use the partition directly using Recovery Manager. It will not give you a true Windows 7 Pro disk, however, but it will restore the factory install of Windows 7.
I assume that is not really what you want because it will be the original Windows 7 Pro without the updates. Trying to get Windows 7 updated will be a chore and take weeks.
So back to the comment "using a generic Win7 Pro disk does not work correctly." Please explain that and then explain what you want to do. Actually using a generic Windows 7 Pro disk, if genuine, should work and will not be any better than a disk from here, but here is a solution for a proper Windows 7 Pro install disk.
https://www.heidoc.net/joomla/technology-science/microsoft/67-microsoft-windows-iso-download-tool
Pick the correct Windows 7 Pro and it will be as best as you can do.
I'm not an HP employee.
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