(a) Notwithstanding any other provision of this part, if a creditor makes a written demand for payment within four months after the date letters are first issued to a general personal representative, the personal representative may waive formal defects and elect to treat the demand as a claim that is filed and established under this part by paying the amount demanded before the expiration of 30 days after the four-month period if all of the following conditions are satisfied:

1. (1) The debt was justly due.
2. (2) The debt was paid in good faith.
3. (3) The amount paid was the true amount of the indebtedness over and above all payments and offsets.
4. (4) The estate is solvent.