Old Asian Vase

This vase has been in the family since the early 1940's.
It is 16 inches h x 10 inches w and maybe made of brass.
What is very unusual is the crude engraving that says "made in Japan".
The engraving does not match the detail workmanship of the vase and looks like it was added to export it out of Japan. My guess is that somehow it was taken out of China to sell on the open market. It is very clear that the engraving was made long after the vase created. Would anyone know the country of origin? Thank you for your interest.