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

Here is Why You Need An Adapter

The outlet and plug type used in Samoa is I and in Liechtenstein are C and J. This is how they look like.

Liechtenstein

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

Type C

Type J

Samoa

In Samoa, outlets of type I are in use.

Type I