The way in which to record this is you would need to receive the payment from the invoice to the business bank account and then do a transfer to the liability account from the business account to show this transaction in Quickbooks.
So go into the invoice>click receive payment> fill in the details needed and choose deposit to would be the business bank account>save and close
Then click on +new top left-hand corner on dashboard> under other click transfer>Transfer Funds From the business bank and Transfer Funds To would be the liability account. Fill the rest of the information in and save and close.
This will show the money has moved from one account to another.