Contract law my arse. He clearly lied to get the contract therefore the contract is invalid.
If anything they have a case against him for obtaining a pecuniary advantage by deception.
If pushed by the FA the directors should immediately place the club in receivership, buy it back for a paltry sum, rename it and put two fingers up to the authorities. This is about people wanting to play and watch football. If all clubs support them then the FA will have FA to go on.