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All Time Tracking Data is stored within JIRA and should be migrated for you by Atlassian automatically. As for app/add-on it have to be reinstalled, and re-configured and all dashboard Gadgets or Email Subscriptions need to be recreated manually.
You may also see https://bitbucket.org/azhdanovtempo-io/jiratimesheetservertimesheet/wiki/Usage_Tracking for information how to find who is using Gadgets, and https://bitbucket.org/azhdanovtempo-io/jiratimesheetservertimesheet/wiki/Migration%20guide for old information what may need to be configured in case of Jira Server
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