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

Here is Why You Need An Adapter

The outlet and plug type used in Cayman Islands are A and B 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

Cayman Islands

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

Type A

Type B