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

Here is Why You Need An Adapter

The outlet and plug type used in Falkland Islands is G and in Lesotho is M. This is how they look like.

Lesotho

In Lesotho, outlets of type M are in use.

Type M

Falkland Islands

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

Type G