Yes, you can absolutely give a gift card to someone who lives abroad.
The BookBeat app works around the whole world. That being said, you can only use the gift card to sign up for the BookBeat market where the gift card was purchased.
Gift cards are only available for the following markets and have to be bought on the respective website: Austria, Belgium, Denmark, Finland, France, Germany, Italy, Netherlands, Norway, Poland, Spain, Sweden, Switzerland, United Kingdom
Gift cards are not transferable between markets.