He is suspected of four counts of supporting the group Jaish al-Muhajireen wal-Ansar, or JAMWA, which was designated as a terrorist organization by the United States last year.
German prosecutors said in a statement Tuesday that the 35-year-old Lau was the go-to contact for extremists wanting to fight for JAMWA in Syria.
He is also suspected of providing financial and material support to the group.
Lau, a convert to Islam, made headlines last year when he attempted to establish a "Sharia police" in the city of Wuppertal to enforce a strict interpretation of Islam.
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