User wants to have the time and expenses entries marked as billed after invoicing them to the client.
Note: The Accounting subscription package is not required for billing as that is controlled by the Billing package.
When creating invoices, all time and expenses that come into the Invoices screen are automatically marked as billed. The only way to prevent this is to either exclude them or mark them billed via the Time/Expense Details option there. Check the Core Help for details.
If you still have unbilled time or expenses after the invoice is created for some reason, you can use the Batch Update option in the Time Entries and Expense Entries screens to mark the selected entries as billed. To cover all entries, this needs to be done in stages, say project by project as you can't select multiple projects view. Or employee by employee, depending on your view.
A better option would be to use the Time & Expense Reviewer screen. Here you can see all time and expenses for all resources over all projects and phases. You just need to select the entries you want to mark as billed and then use Actions > Mark Billed. Check the Core Help for details.