Hi,
Posted Purchase Receipt is only a Receiving Document for goods/services while Payment is made for financial document that is Posted Purchase Invoice. You can get a record of all Invoices and Payments from Detailed Vendor Ledger Entries.
System will not Invoice same quantity again. The rule is we cannot Invoice a quantity unless it is received and directly there is no relation from Posted Purchase Receipt to Posted Purchase Invoice. Its reason is one Purchase Receipt can be Invoiced in multiple Invoices or one Posted Purchase Invoice is for many Purchase Receipts. Posted Purchase Receipt has Purchase Order No. and then from Purchase Order you can find all the Receipts and Invoices posted.
Additionally in Purchase Order line you have fields to see Quantity, Quantity to Receive, Quantity Received, Quantity to Invoice and Quantity Invoiced.