Go to Issues -> Search, and run a filter for the issues you want to assign to the user.
Then, from the tools menu (near the top right in the results section), use "bulk edit" to edit the issues, setting the assignee.
You need to have the right to assign the issues you select, and the global permission for "bulk edit" to be able to do this. Ask your admins if the bulk edit option is not on the menu.
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