I am moving permanently from the US to Brazil.
How can I make all my letters be forwarded from my old US address to my new Brazilian address?
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International Mail Forwarding is what you'll be after. Most major national postal services offer it, for a fee
Not so well explained on that bit of the site is the international part. If you go to the USPS FAQ entry on Change of Address - General Information, then scroll down quite a bit, you'll find this helpful piece:
How do I file a Change of Address for an international address?
You cannot submit a Change of Address online for an international address.
If you are moving to an International address outside of the United States, you will need to fill out the same Change of Address (COA) form (PS Form 3575) that is filed for a domestic move at your local Post Office™.
So, you'll need to fill out the form mentioned, head to your local post office, and arrange + pay for the international mail forwarding in person.