This is a manual process - you'll need to search for and reassign all issues to the new user, and edit the reporter of issues reported by the old one. Also custom fields that contain users, watchers, participants, appprovers and so on. The permissions will need to be scanned through manually, adding the new user wherever you find the old one (although it's a terrible practice to use individuals in permissions, you might have done it), and notifications, and security schemes.
You'll need to edit the database if you wish to update the ownership of comments or historical records.
This is not a small undertaking, you might find it easier to just shut down the old user, transfer the minimum (reporter and assignee) and leave the rest.
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