Is it sufficient for a staff member who has lied on his CV to inform the first two responsible managers about his lie after repenting, or must he inform the two new responsible managers?

What this person did, in repenting and informing his employers about his falsehood in his CV, is sufficient for him. He is not obligated to repeat that with every new official or manager. There is no blame upon him for remaining in his job as long as he performs it skillfully and as required.