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The UI will pop-up messages when a bill run starts and when it finishes. When a bill run finishes it will generate an invoice (provided run & render invoices was set on the bill run, and there were charges on the account to bill). After the bill run finishes you can load the Invoices screen to view the invoice details (transactions on it, taxes applied, etc.). To view the invoice you can download it as as a pdf on the same Invoices screen (using the 
action button).