Linda,
As Randy mentioned, the label itself is saved as part of the file, so it persists no matter where the document is stored. It depends on the controls you configured for the label as to what happens in that environment. If you turned on encryption as part of the label control, then you're either forcing the person opening the file to authenticate back to O365 and you're potentially restricting who within your population can decrypt the document, so they might need to be in a particular group - it all depends on how you choose to protect the labeled file.
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Peter Rahalski, CIP
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