A local unit of Panama law firm Mossack Fonseca & Co. has been fined $440,000 by the British Virgin Islands financial regulator after a probe sparked by April’s “Panama Papers” data leak.

Anti-money laundering and terrorist financing controls were inadequate at Mossack Fonseca & Co. (B.V.I.) Ltd., and customer risks weren’t always assessed, the BVI Financial Services Commission said in an enforcement action published on its website. Customer identification wasn’t always checked when business came to the Mossack Fonseca office...