Yes, you can. On March 23, 2013, the ten largest transit smartcards in Japan became fully(*) compatible, and this includes Pasmo, Suica and all three systems used in and around Fukuoka: Sugoca (JR Kyushu), Nimoca (Nishitetsu) and Hayakaken (Fukuoka City Subway).
(diagram courtesy of JR East)
(*) For tickets, anyway, electronic money is a little more complicated, and there's a long tail of non-top-ten cards that are only partly compatible. See this diagram with oh-so-many arrows on Wikipedia for the gruesome details.