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

Here is Why You Need An Adapter

The outlet and plug type used in Falkland Islands is G and in Réunion are C and E. This is how they look like.

Réunion

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

Type C

Type E

Falkland Islands

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

Type G