Singapore Airlines offer a direct flight between Fukuoka Airport and Singapore Changi Airport every day. It takes 6 hours 15 minutes from Singapore to Fukuoka by direct flight and 6 hours and 25 minutes from Fukuoka to Singapore. The airport is directly connected with subway lines, taking you to central Fukuoka in just 5 minutes. You can get to the downtown shopping area in about 10 minutes.

Singapore Airlines
https://www.singaporeair.com/en_UK/sg/home

Fukuoka Airport
http://www.fuk-ab.co.jp/english/