FAROE ISLANDS is not part of the Schengen area.
A visa to enter DENMARK or another Schengen country is not valid for entry into the FAROE ISLANDS.
A visa for DENMARK does not give the holder the right to enter the FAROE ISLANDS unless it is stated on the visa, just as a visa for the FAROE ISLANDS does not give the holder the right to enter DENMARK, if it is not stated on the visa. Visa is required for entering the FAROE ISLANDS regardless of the person having a residence permit in DENMARK. Correspondingly, a visa is required when entering DENMARK, even though the person has a residence permit in the FAROE ISLANDS.