Yes. Your record is with MoM.

Are u holding work pass? from my experience is that the new company apply EP for me, it require my previous FIN number..if u fill in previous FIN number then your new employer will find out lo..if u don't fill in previous FIN then MOM will find it fishy then lagi kantoi 

All records are recorded in MOM.

In order to take on your next job you would require a new employer to update and replace the old company for sponsoring your EP visa.

Lying will get you no where. It only makes thing worst, just state another good reason to move. But in such case, even your new company will be in doubt because it shows that you dont have commitment to the old company. Unless the new company is interested in you, better not jump into the sea assuming you got a boat on the other side to land.