Bigger jobs rarely get paid all at once. From an invoice, you can split the total into installments: a deposit up front, milestone payments while the work runs, and a final amount at completion. Each installment is its own invoice linked to the original, so the customer sees exactly what is due now.
The original invoice's status updates as the installments are paid. Record each payment as it arrives, with the method your customer used, and the Overview shows what is still outstanding. Reminders for each due date are local notifications that open a message draft. You decide whether to send it, and nothing goes out automatically.
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