I'm assuming you want to try and preserve at lease some of the technical context/history of what appear to be "simple documents" in the SharePoint site. If so then it's best to use a migration tool, rather than trying to slice files off of the
IIS web interface and ignoring deeper things powering SharePoint from the background like the Active Directory users and groups, SQL databases and SharePoint central administration configurations, etc.
Hopefully you donor organization will donate some of their IT Pro SharePoint Administrator time, so that resource can help you run some PowerShell queries, interpret any error messages that come up in the error logs, plan workarounds, etc.
Best of luck, hopefully someone else here has a better / more precise answer for you!