You Do Need power plug adapter while traveling from Falkland Islands to Solomon Islands.

Here is Why You Need An Adapter

The outlet and plug type used in Solomon Islands are G and I and in Falkland Islands is G. This is how they look like.

Falkland Islands

In Falkland Islands, outlets of type G are in use.

Type G

Solomon Islands

In Solomon Islands, outlets of type G and I are in use.

Type G

Type I