Generally speaking, you can claim against both insurers, but you can only recover the loss once.
The merchant has a choice of either taking the “enhanced protection” service offered by most couriers or opting for the Anansi insurance product, which would replace the additional "enhanced protection fees" charged by the shippers, so there should not be a double insurance situation.
However, if any indications of insurance fraud are detected by the Anansi system, we would need to investigate.