Even though Arthur is a former employee and no longer an insider, he is still subject to the 16(b) short swing profit rule. He can't make a discretionary sale for 6 months following his last "purchase."
I don't recall him getting any new grants of stock or new option grants
(which would be considered purchases even if non-vested) when he got the new employment contract in January.
If my memory is right, Arthur would accordingly have no sales restriction and no Form 4 reporting requirement after leaving. (The acceleration of vesting for his options due to termination w/o cause is not a "purchase.")
Of course, if he has special inside knowledge he can't sell due to the anti-fraud restrictions of rule 10b-5.
This is memory, so if you happen to be a corporate insider of a public company, don't make any short-swing transactions based on this!