en.wikipedia.org/wiki/Free_City_of_Danzig

This wording overstates what the Allies decided at Potsdam.

The Potsdam Protocol said that, pending the final determination of Poland's western frontier, the former Free City of Danzig "shall be under the administration of the Polish State". That is not the same as being definitively "awarded" to Poland.

Contemporary U.S. diplomatic records make the same distinction. On 8 May 1945, the U.S. State Department stated that the Free City of Danzig and other occupied German territory under Polish administration "remain in fact enemy territory under Soviet military occupation" pending later agreements among the Allied powers.

So the article's infobox claim is inaccurate in two ways:

1. it describes the Potsdam decision as a final transfer ("awarded"), even though the official language was provisional administration pending a final settlement; and
2. it gives a precise date for a final award that the cited agreement itself does not make.

The Potsdam Agreement did not state that Danzig was definitively incorporated into Poland.

Its text says that, pending the final determination of Poland's western frontier, the area of the former Free City of Danzig "shall be under the administration of the Polish State". That is provisional administrative control, not a completed legal integration.

Contemporary Allied diplomatic documents explicitly preserved that distinction. A U.S. State Department telegram from 8 May 1945 stated that the Free City of Danzig and other occupied territory under Polish administration still "remain in fact enemy territory under Soviet military occupation" pending later Allied agreements.

So saying the city was "fully integrated into Poland due to the Potsdam Agreement" is stronger than the agreement itself and misdescribes the legal status created at Potsdam.