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

Here is Why You Need An Adapter

The outlet and plug type used in Saint Helena is G and in Pitcairn Islands is I. This is how they look like.

Pitcairn Islands

In Pitcairn Islands, outlets of type I are in use.

Type I

Saint Helena

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

Type G