Many of the responses to this question seem to have overlooked the fact that the OP said they are using cash-basis. With cash-basis there isn't really supposed to be accounts receivable or accounts payable. Income is earned when funds are received, not when billed through an invoice.

What I've found is that QBO does have a AR account, some reports make reference to it, and you can look at it in the chart of accounts. So. Lots of opportunity for confusion.

What I do is create an invoice, and send it out (I like that QBO does that legwork for me). When I receive funds (e.g. through direct deposit) from a customer, instead of "add"ing the transaction as a deposit, I first go to the invoice, and do "receive payment". When I go back to the Banking page and look at transactions, it offers to match the bank transaction with the "Payment" I made.

After doing all that, on a P&L, I will see income reported. When you click on it, you'll be taken to the Invoice (even if it was from only a partial payment), not the deposit, or whatever transaction shows in the bank account register. Note that I don't have to do anything to the AR account. I suspect it is being manipulated behind the scenes by QBO. But it doesn't show up in P&L, nor Balance sheet. I get the appearance of real cash-basis accounting.