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

Here is Why You Need An Adapter

The outlet and plug type used in Liechtenstein are C and J 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

Liechtenstein

In Liechtenstein, outlets of type C and J are in use.

Type C

Type J