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If the dates are configured to be edited, you can edit the Started On and Finished On dates by clicking in the calendar icon and choosing the date and time. You can check your configurations by going to JIRA ADMINISTRATION > Add-ons > Global Preferences.
Note: The JIRA jira.date.time.picker.java.format and jira.date.time.picker.javascript.format should belong to the same pair of properties in order to the datetime picker work properly. See the following link for more information
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