When you receive the check and enter it as a deposit in AR-N, the program will Debit Cash (either the bank or undeposited funds, whichever bank account you choose) and credit Customer Deposits.  If you enter a payment in AR-C and do not apply it to any invoices and then save it, you are prompted whether it is a Deposit or a Credit.  If you choose Deposit, the same GL posting occurs.  If you choose Credit, then the program will debit Cash and credit AR.
 
When the invoice that the AR-N deposit is applied to is posted, you will get a debit to Accounts Receivable for the total invoice amount, then a credit to AR and a debit to Customer Deposits for the applied deposit amount so the net open AR matches the net balance due on the invoice.