Do not recharge the customer unless you obtain a new signed ACH Authorization Form.
An R10 "No Authorization" ACH reject means that your customer told his/her bank that s/he never allowed your business to charge his/her bank account. Therefore, the customer's bank took the money back from your business and gave it back to your customer. For this reason, it is extremely important to obtain a signed ACH Authorization Form for every ACH transaction.
In order to claim that the ACH transaction was "not authorized", your customer must go to their bank and complete a Written Statement of Unauthorized Debit (WSUD). The WSUD is a legally binding affidavit. The customer is claiming, under penalty of perjury, that s/he did not authorize the transaction. Therefore, theoretically, if the customer goes to this extent, it must be true that the customer never authorized the transaction. However, if the customer is not truthful, they can be taken to court for theft/fraud. For this reason, R10 rejects are very rare.
If your business did obtain a signed ACH Authorization form, then you are able to request a copy of the Written Statement of Unauthorized Debit (WSUD). With a copy of the WSUD, you can file a lawsuit against this individual for theft/fraud.
Note, the Written Statement of Unauthorized Debit (WSUD) must be requested within 1 year of the R10 reject. Please contact PayJunction Customer Support in order to request a copy of the Written Statement of Unauthorized Debit (WSUD).