Banking Policy? Please help!

chillertwist

Hi all,
I hope somebody can assist.

Right where to start. I arranged for a transaction online from my account to my sister in laws. She provided the account number and sort code which I used for the transaction.
The money has since been debited from my account however she has not received and has now realised she provided the wrong bank account (Daft (to say the least) I know).
I have been advised by my bank (Co-opertaive) that there is nothing they can do as the money has cleared in to a live account at Lloyds.
This is the same bank as my sister in law and obviously to an account at the same branch as her.
She has contacted her bank and explained the situation and has suggested that the bank could contact the account holder of where the money has been deposited and request that it be returned (fully aware no inital obligation for that account holder to do so). However Lloyds have declined and stated that they can do this and have no right to access this other persons account etc and have also fobbed her off stating that it is up to my bank to recall the money.
I have also been advised that if the account holder who has received the transfered money was aware or had been informed about the problem and declined to return it that there are actually criminal procedures that could commence as there are offences of Theft and / or Fraud.
Ultimately I would like any advice about the matter and also what each bank should be doing in this situation.
We have tried the usual tatctics of being patient and understanding and have tried to reason with them and use logic but to no avail HELP!!!!!!!!!!!!!!