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

Here is Why You Need An Adapter

The outlet and plug type used in Saint Barthélemy are C and E 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

Saint Barthélemy

In Saint Barthélemy, outlets of type C and E are in use.

Type C

Type E