Sir, I would like to tell you that it would be okay if ADT-3 is not filed as there is no resignation as such (but during our management training we were instructed to file ADT 3 for situations as in your case)
But ADT-1 has to be filed in any case as it is a clear cut case of casual vacancy under section 139(8) of the Companies Act, 2013. Now the Auditor cannot practice in his individual capacity so it is a case of casual vacancy. This has to be filled by the Board and ADT-1 will be filed.
Further, a question may arise while filing ADT-1 for the appointment of Audit Firm to fill the casual vacancy as to what shall be written in SRN of relevant form( which is asked in case you say yes to the question whether auditor is appointed to fill the casual vacancy), i tell you to fill the SRN of ADT-1 of individual auditor.( I am telling this because mostly people fill the SRN of ADT 3 but adt 1 help kit instructs to fill the SRN of ADT 1).
As we know the the Auditor appointed to fill the casual vacancy holds office till the conclusion of next AGM. Hence ADT 1 at the AGM will also be filed for further term.
Thank You