You Do Need power plug adapter while traveling from Puerto Rico to Cocos (Keeling) Islands.

Here is Why You Need An Adapter

The outlet and plug type used in Cocos (Keeling) Islands is I and in Puerto Rico are A and B. This is how they look like.

Puerto Rico

In Puerto Rico, outlets of type A and B are in use.

Type A

Type B

Cocos (Keeling) Islands

In Cocos (Keeling) Islands, outlets of type I are in use.

Type I