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

Here is Why You Need An Adapter

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

Solomon Islands

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

Type G

Type I

Guam

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

Type A

Type B