Here's a short list of the versions of Movie Maker you might encounter:
- Windows XP -- Windows Movie Maker 2.1
- Windows Vista (insufficient GPU) -- Windows Movie Maker 2.6
- Windows Vista (GPU capable) -- Windows Movie Maker 6.0
- Windows 7/8.1/10 -- Movie Maker 2009/2010/2011/2012.
Versions 2.1, 2.6 and 6.0 create a project file with an extension of .mswmm.
Versions 2009 to 2012 create a project file with an extension of .wlmp
A project file from 2.1 can be opened in 2.6 or 6.0
A project file from 2.6 can be opened in 6.0
A project file from 6.0 can be opened in 2009-2012.
A project file from 2009/2010/2011 can be opened in 2012.
But project files aren't *backwards* compatible. In other words, once you open a project file from a newer version and save it in that version, it can no longer be opened in an earlier version.
You didn't explain exactly which version you have loaded on Windows 10. For example, you could still load Windows Movie Maker 2.6 on Windows 10 and it should open/save the project without problem.
But if you have a newer version (e.g. WMM 6.0) the saved file would not be able to be opened again on the older version.
Basically all you need is the backed up copy of the project from WMM 2.6 and it will still be able to open in WMM 2.6 on an older system (assuming you have all the same source files also still on the computer).
So can you explain exactly which version of Movie Maker is on each PC and whether you saved in that version or not?