US QuickBooks Online Edition
Is it possible to attribute (connect) a submitted invoice to a customer to the actual payment transaction which was deposited in my business account in my bank?
If you have created Invoice (Customers > Invoice), it will save as outstanding (or unpaid) invoice. So, you need to receive payment (Customers > Receive Payment) in order record as payment from this customer as well as deposited to your chosen Bank Account. That will complete the entry for this transaction.
You can create Sales Receipt (Customer > Sales Receipt) for all already paid invoice (bill) by the customer.