You Do Need power plug adapter while traveling from Falkland 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 Falkland Islands is G. This is how they look like.

Falkland Islands

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

Type G

Saint Barthélemy

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

Type C

Type E