This Kb serves as a brief explanation on how the migration works for the Prime plugins from Jira Server/DC to Jira Cloud, using Jira Cloud Migration Assistant.
This serves either for Timesheet Reports and Gadgets for Jira Server/DC and Time Reports for Jira Server/DC.
Instructions
Since all Time Tracking and Issues data are stored in Jira Database, no Data will be lost, please refer to this KB How intrusive is Timesheet plugin in JIRA? , the migration should be as straightforward as to migrate Jira Software itself;
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. See this Kb Cloud/Server Moving/Migration for more information. you could use Jira Cloud Migration Assistant to migrate from Server to Cloud. Refer to this KB https://support.atlassian.com/migration/docs/use-the-jira-cloud-migration-assistant-to-migrate/ for more information.