No offense, do not take it personal. It is a good example ...
Nope.
He could exercise the option anytime (independently from the pps). He will exercise because the option will expire on 11/10/2020 (the $3.40 is the exercise price) and / more likely / the pps will be higher than $3.40.
(More likely) Form-4 (if he will not sell immediately):
M 750.000 @ $3.40 (the Reporting Person was granted 750,000 options on xx/yy/zzzz under the Amarin Corporation plc Stock Incentive Plan
A 750.000 @ $3.40
F xxx.xxx @ market price on the Transaction Date (Represents withholding by the Issuer of shares in respect of tax liability incident to the vesting of a security issued in accordance with Rule 16b-3, and not a market sale of securities.)