Hi Esther,
Grajewo (in Lomza gubernia) and Augustow (in Suwalki gubernia) were right on the border with Konigsberg in East Prussia, a major Baltic port. A lot of people smuggling took place in the last quarter of the 19th century in this way. In WW1 this area was overrun by the German Army and it was part of the WW1 front line (same in WW2 as well). So it is likely your ancestor found their way to Konigsberg Port.
All my great grandparents came from this area to UK between 1865 and 1875.
Jill Whitehead, Surrey, UK