Hi,
I find it slightly strange that the letting agency are chasing you for this bill, when in fact it's the power company that should be doing this? As per regulations, it's the resident of the property that is responsible for the final balance, not the owner or landlord. All the letting agency would have to do would be to prove (using letting agreements etc) that they were not responsible for the supply.
As such, the letting agency that's somehow in Belfast would have no obligation to pay this bill on your behalf, and therefore should not be chasing you.
An SAR is certainly a good idea. Additionally, contact the bank and ask for a printout of the month that the final bill would have been paid. If you can show that you paid the balance to the power company, then it could be that they credited it to the wrong account/meter serial no. Contact the power company and state that the account is in dispute and that you would like them to provide all details necessary.
As your sister was the account holder, you'll either need her to contact the company, or, phone up with her present, and have her confirm over the phone to the operative that she is happy for you to deal with her account.