On the 8th he made his debut, replacing Llorente for the last 15 minutes of a 3–1 home win against Lithuania.
On October 15, 2013, Zwayer has refereed 2014 FIFA World Cup qualification match between Lithuania and Bosnia and Herzegovina national football team in Kaunas.
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Everything seemed to be going well, but Fortunato caught pneumonia and was never able to recover – he died on 25 April 1995 on the eve of Italy’s game with Lithuania in Vilnius.
He scored his first international goal in a 5-2 win in Podgorica and the scored again in a 1-1 draw at home to Lithuania.
On 11 October 2011, he made his debut for the Lithuania national football team in a UEFA Euro 2012 qualifying Group I match against the Czech Republic.
He made his international debut for Liechtenstein on 13 October 2012 against Lithuania, coming on as a substitute for Philippe Erne.