A man who travels between the the US and Canada and has places in both countries takes several firearms to Canada. He is subsequently served with a US criminal summons that alleges he transgressed federal law, but contains no specific citation.
If "places" = homes located in both the U.S. & Canada, and legal occupancy in both countries;
and purchase of said firearms in the U.S. was in compliance with federal/state/local laws;
and if bringing the firearms into Canada complied with Canadian law;
and the firearms in question are legally owned/purchased by the traveler;
then the traveler needs to contact an attorney and the agency/agencies listed in the criminal summons, in that order.
Except for a few hinky exporting laws, I can't think of any reason why a U.S. law would have been broken. But even then, if it is an individual transporting the firearms from a place of legal status/residency in the U.S. to a place of legal status/residency in another country, then it doesn't pass the sniff test/definition of exporting. As long as it remains in the possession/ownership of the traveler, he/she has not exported anything...
Export -
1.
to ship (commodities) to other countries or places for sale, exchange, etc.
2. to send or transmit (ideas, institutions, etc.) to another place, especially to another country.
3. Computers . to save (documents, data, etc.) in a format usable by another software program.
verb (used without object)
4. to ship commodities to another country for sale, exchange, etc.