I have a user who posts a shared workbook on a share where the permissions are open. This is supposed to be a temporary posting place. The idea was that users from multiple groups could open the file with the sheets locked and the updates could be added by a user with the password.

However, if a person tries to open the file when someone is in the document they get this notice.

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The user would like to be able edit the document and not get this message. Is this possible?

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why don't you use the shared feature? you can assign the user permission of the sheet range see here https://support.office.microsoft.com/en-us/article/Use-a-shared--workbook-to-collaborate-b8207fe9-a613-483f-b804-0ca4658b0c61?CorrelationId=794a97fd-60f2-4699-a2d7-40a4e2d1d708&ui=en-US&rs=en-US&ad=US