Ship Movement Question Axis and Allies 1940 Global (Rules 2.0)
Here is a 2 part answer to your question: 

From the Rules (http://www.axisandallies.org/wp-content/uploads/2011/12/Axis-Allies-Pacific-1940-Second-Edition.pdf):


  Move as many of your units into as many hostile territories and sea zones as
  you wish. You can move into a single hostile space from different spaces, as
  long as each moving unit can reach that space with a legal move.


I added in bold the important part. During your combat move, you can move into a single, hence only one hostile space. So no he cannot continue to move to a second hostile territory afterwards. 

From the Non-combat move rules: 


  In this phase, you can move any of your units that didn’t
  move in the Combat Move phase or participate in combat
  during your turn


Once again in bold, units that DIDN'T move can move in the non-combat phase.

Exception: I know that your question was about sea units, but tanks have a special "blitz" ability which allows them to continue moving after combat. Just look for the "blitz" ability in the units part of the rulebook.   

Hope this answers your questions.