Your problem in a nutshell is: the liability account is wrong for your invoice. Invoice is validated and approved and the payment has been made.

Invoice Accounting:

DEBIT: EXPENSE
CREDIT: WRONG LIABILITY ACCOUNT

Payment Accounting:

The wrong liability account has been propagated to your payment accounting as well.

DEBIT: WRONG LIABILITY ACCOUNT
CREDIT: CASH

One option is:
1) Void the payment
2) Cancel the invoice
3) Re-enter another invoice
4) Repay this invoice (Use dummy wire payment if the check has already mailed out).

Option 2:

Pass an adjusting entry in GL for invoice accounting correction:

DEBIT: WRONG LIABILITY $x
CREDIT: CORRECT LIABILITY ACCOUNT $x

Pass an adjusting entry in GL for payment accounting correction:

DEBIT: CORRECT LIABILITY ACCOUNT $x
CREDIT: WRONG LIABILITY ACCOUNT $x

If the payment is made in the same period as the invoice GL date then your wrong liability account is will not have any balance for that period. The adjustment entries may not be necessary. Accountants should make a call on how to fix this.