Showing transactions on your invoice can provide some additional information that your clients will want to see, including a breakdown of payment if credit is applied to an invoice.
To enable transactions on the invoice email you need to navigate to Settings - Company - Email Templates and select Billing Emails from the drop down and edit Payment Receipt Template and add the tag [PMTTRANSACTIONS]
To add transaction records in the PDF file you need to navigate to \plugins\invoices\[yourinvoicestyle]\invoice.phtml and around line 112 change
<!-- <div><?php echo $this->unescape($this->pmtTransactions); ?></div> -->
<div><?php echo $this->unescape($this->pmtTransactions); ?></div>
Simply un-commenting the code.