Can a foreign supplier product declare a cash register system, even if the sale of the system is made through a Norwegian agent?

It is the supplier of the cash register system who is supposed to product declare the system. A supplier is defined in the Cash Register System Act section 2 letter e:

A producer or an importer who either them self or through a distributor sell or offer a cash register system etc. for sale, lease or lending to an enterprise with a bookkeeping obligation as mentioned in section 1, and distributors and others who adjust cash register systems for the enterprises with a bookkeeping obligation.

When an importer of the cash register system does not make any adjustments to the system, the foreign supplier product declares the system. If the foreign supplier fails to do so, the importer must see to that a product declaration is made.