I am a US citizen and I received an academic prize in Italy, which was taxed at a rate of 25%.
No official documents where provided to me.
How do I file this in my 1040 and how do I get credit for the tax that I already paid in Italy? (I know there is a tax treaty between the US and Italy)

You claim the income on Line #21 of Form 1040 as "other income".

You then file Form 1116 to claim the Foreign Tax Credit for the 25% tax you paid to Italy. Since this is passive income, you should get a dollar-for-dollar credit.

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