@NotableLive 

Can you explain more?  A bank transfer cannot be used to clear an invoice because A/R is not involved.  To clear an invoice, you need to credit A/R and debit another account (generally a bank account).  That is done with the Receive payment function.  A bank transfer simply credits bank account 1 and debits bank account 2 and never hits A/R.  If you're trying to clear an invoice, you should have a payment received from a customer, not just an internal company transfer.  Presumably, there's more to the situation...      

Several one-off client transactions were paid to our PayPal account. My boss had me invoice PayPal as a customer in August, enabling the A/R to show as invoiced income. In September, a transferred was made to our operational bank account from the PayPal account (which is listed as a bank account in QuickBooks on-line). The activity was correctly reconciled as a transfer, but the invoice still shows outstanding.

@NotableLive 

When the payment on the invoice was received into your PayPal (PP) account, did you not use Receive payment (New > Receive payment) and select your PP account under the 'Deposit To' drop-down menu?  That deposits the payment into your PP account and closes the invoice.  Then, just transfer the funds from PP to your operational bank account using New > Transfer.  The invoice should have been cleared when payment was received into your PP account, not when transferring from PP to your operational account.