Mr Moore, who replaced Mr Rheinberg as senior coroner in March 2017 and retired himself in June 2022, added: "The provision of timely, accurate and truthful information is fundamental to the coronial process.
"If the Countess of Chester had become aware of any information which had not already been disclosed to the coroner's office that would impact upon a death, the Countess of Chester would have been required to disclose that information immediately.
"The Countess of Chester would have been expected to notify the police immediately if it had any reason to suspect that a person or persons may have been criminally responsible for causing a death.
"The coronial process is a judicial process. It demands complete candour from healthcare professionals, clinicians, nurses and from hospital staff and also from trust management.
"A failure to disclose to the coroner any information which may have a material bearing on a coronial case, whether it's been through the coronial process already or is pending, is to mislead the coroner and to mislead the court."
Letby, 34, from Hereford, is serving 15 whole-life orders after she was convicted at Manchester Crown Court of murdering seven infants and attempting to murder seven others, with two attempts on one of her victims, between June 2015 and June 2016.
The inquiry, sitting at Liverpool Town Hall, is expected to sit until early 2025, with findings published by late autumn of that year.