There is always the possibility that the set was made by or for a German or Austrian in Finland, which would account for the typical Germanic elements and the Finnish mark. The work doesn't look Finnish in a cultural sense but the marks still would represent its place of manufacture.
Something along the lines of what are you if you are born in a foreign country of English parents.
I would consider it a multi-national piece. The item seems to have traveled around the world! Austria, Germany, Finland, Mexico and Spain.
But can it be explained as simply Fininish by the 813 mark?
No, the item is not Finnish. If it would be Finnish it would have the complete set of hallmarks with the crown, purity etc. Also the purity is marked with 813H and not with only the number 813. Numbers neither look like on Finnish hallmarks.