You Do Need power plug adapter while traveling from Azores 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 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

Faroe Islands

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

Type C

Type E

Type F

Type K