You Do Need power plug adapter while traveling from Cayman 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 Cayman Islands are A and B. This is how they look like.

Cayman Islands

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

Type A

Type B

Solomon Islands

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

Type G

Type I