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

Here is Why You Need An Adapter

The outlet and plug type used in Saint Helena is G and in Martinique are C, D and E. This is how they look like.

Martinique

In Martinique, outlets of type C, D and E are in use.

Type C

Type D

Type E

Saint Helena

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

Type G