You Do Need power plug adapter while traveling from Fiji to British Virgin Islands.

Here is Why You Need An Adapter

The outlet and plug type used in British Virgin Islands are A and B and in Fiji is I. This is how they look like.

Fiji

In Fiji, outlets of type I are in use.

Type I

British Virgin Islands

In British Virgin Islands, outlets of type A and B are in use.

Type A

Type B