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

Here is Why You Need An Adapter

The outlet and plug type used in Puerto Rico are A and B and in Azores are B, C and F. This is how they look like.

Azores

In Azores, outlets of type B, C and F are in use.

Type B

Type C

Type F

Puerto Rico

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

Type A

Type B