You Do Need power plug adapter while traveling from Balearic Islands to Saint Helena.

Here is Why You Need An Adapter

The outlet and plug type used in Saint Helena is G and in Balearic Islands are C and F. This is how they look like.

Balearic Islands

In Balearic Islands, outlets of type C and F are in use.

Type C

Type F

Saint Helena

In Saint Helena, outlets of type G are in use.

Type G