Isak made waves with a string of exceptional performances for the AIK first team in 2016, leading to several big clubs chasing his signature. Dortmund ultimately beat the competition.
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AIK have now been ordered to pay 350,000 kronor ($39,700) following the transfer of the 17-year-old rising star of Swedish football to the German club in January however.
The club protested that world football governing body FIFA – which approved the transfer – failed to spot the payment.
FIFA transfer rules prohibit players and clubs from making payments to agents for under-age players.
“Our experience of selling under-age players internationally is very limited and we trusted … We'll know better next time,” the club said in a statement.
Forward Isak, who turns 18 in September, has already won two caps for Sweden, scoring one goal. He has played just a few minutes with the Dortmund first team in the German Cup.