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Hi Wallace,
How do you copy/move the mpp file? Could you give us some detailed steps? For the symptom of the issue you have met with, could you give us some screenshots?
Generally, if you activated the SharePoint Server Publishing Infrastructure and use the Content and structure feature, you can move or copy the file with the same version.
For your reference: https://support.office.com/en-us/article/Work-with-site-content-and-structure-30fcaad9-02b1-4347-8b03-e1ccc5a4c19f
Note: The article is often applied to SharePoint Online.
Please let us know your updates at your convenience.
Thanks,
Cliff