You Do Need power plug adapter while traveling from Falkland Islands to São Tomé and Príncipe.

Here is Why You Need An Adapter

The outlet and plug type used in São Tomé and Príncipe are C and F 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

São Tomé and Príncipe

In São Tomé and Príncipe, outlets of type C and F are in use.

Type C

Type F