Yes, the move retains all the watchers.
However, if you do not have the permission to see the new project, updates will not be sent to you, as you can't see the issue any more. But you're still a named watcher and if you get access to the project, updates will resume. Also, the new project may have a notification scheme that does not notify watchers - again, you're still watching, but you won't be sent emails.
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