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

Here is Why You Need An Adapter

The outlet and plug type used in Faroe Islands are C, E, F and K 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

Faroe Islands

In Faroe Islands, outlets of type C, E, F and K are in use.

Type C

Type E

Type F

Type K