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Check whether your browser's version is supported for the Capture for JIRA browser extension on Capture for JIRA Compatibility Chart. Note that Capture for JIRA does not currently support any mobile browsers (iOS, Android, etc).
You will also need the Capture for JIRA plugin installed on your instance of JIRA before the extensions become available. Otherwise, you will not see the 'Test Sessions' menu in your JIRA site.
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