The best process for recording invoice payments, no matter if for one or for many invoices, is by recording a single New Customer Payment transaction in your Customer Invoice account. This process will allow you to select which invoices have been paid and to correctly mark them as such. When done you will find a deposit transaction in your checking account in the amount of the check. Now you can go to the bank and deposit the check.
If payment were to arrive in the form of an electronic deposit in your checking account, you need to record the New Customer Payment transaction BEFORE downloading from the bank or BEFORE accepting downloaded bank transactions into your checking account register. This way Quicken can match the downloaded transaction to the already existing register transaction.
If you have (somehow incorrectly) received payment for the customer and invoices remained as unpaid, you can correct that problem. Record a $0.00 New Customer Payment transaction in the Customer Invoices account, click to put a checkmark into the "Apply existing credits" box and mark all unpaid invoices as paid. Save the transaction. You will not find a $0.00 payment transaction in the register, but all marked invoices for this customer will now show "c"(cleared) in the Clr column and should be taken off the unpaid invoices list.