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After you are done editing the document, click save on the document, close out of the document and then click save on the box above where it reads "Click here to save this document back to ProjectID ----". This will make the document that you originally opened as not current and add the edited document automatically back to e-manage as current so you have a history. You can convert back to the previous document by checking the current box and unchecking the document you want to make not current.
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If you are not getting this popup, please ensure that the type of document you’re trying to edit is editable. Check this by going to Documents (top toolbar) > Configure Editable Document Types and mark the type of document as editable.