What is the crowd's opinion of SubInACL?

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For something similar, I found subinacl to be more friendly to use than powershell. Handy reference

You could try RepACLs or Microsoft's SubInACL to migrate your users

Are you logged in a domain administrator, or just local admin on the file server?

Try logging in as whatever service account your backup process runs as ;)

Or just give yourself permission to all the files beforehand, but don’t do it manually, use subinacl - https://social.technet.microsoft.com/wiki/contents/articles/51625.subinacl-a-complete-solution-to-configure-security-permission.aspx