You Do Need power plug adapter while traveling from Puerto Rico to Saint Barthélemy.

Here is Why You Need An Adapter

The outlet and plug type used in Saint Barthélemy are C and E 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

Saint Barthélemy

In Saint Barthélemy, outlets of type C and E are in use.

Type C

Type E