... player to play for a country which isn't their place of birth
As in how much they contributed to that nations football e.g. Pioneer (First black player), Made people take more notice of that country (this can work in many ways) etc etc
I'm going to give some examples but I am not saying any of them are the greatest:
(Born/Country Represented)
Maurice Tresor (Guadeloupe*/France)
Patrick Vieira (Senegal/France)
Mohamed Sissoko (France/Mali)
Paul Chillan (Martinique*/ France)
Fredric Kanoute (France/Mali)
John Barnes (Jamaica/England)
Robbie Earle (England/Jamaica)
Clarence Seedorf (Surinam/Holland)
Chris Birchall (England/Trinidad & Tobago)
Anthony Baffoe (Germany/Ghana)
Yıldıray Baştürk (Germany/Turkey)
Eusébio (Mozambique/Portugal)
Alfredo di Stéfano (Argentina/Played for Argentina, Colombia and Spain LOL)
One thing I do notice about the players that come to my mind is that they moved to the country they represented very early in their life. It is rare you'll find someone you made an significant or memorable impact who didn't live in that country for long period of time, if at all.... (excluding Robbie Earle - 1st World Cup Goal Ever or Birchall's 'Belter' against Mexico)
*(I know that Gwadloup and Mantik are dependencies of France)