Is the word remetente the same in Brazilian and European Portuguese?

Yes

The word "remetente" is identical in both Brazilian and Continental Portuguese regarding its spelling, meaning, and grammatical classification (noun). The only difference is pronunciation: Brazilian Portuguese tends to pronounce the vowels with more openness and clarity, whereas Continental Portuguese features significant vowel reduction, where unstressed vowels (such as the final "e") are often shortened or nearly silent.

Brazilian Portuguese examples:

1. O remetente esqueceu de assinar o pacote. (The sender forgot to sign the package.)
2. Você conferiu o endereço do remetente? (Did you check the sender's address?)
3. O remetente não colocou o CPF no formulário. (The sender did not put the CPF on the form.)
4. Recebi um e-mail de um remetente desconhecido. (I received an email from an unknown sender.)
5. O remetente não mandou o comprovante. (The sender didn't send the receipt.)

Portuguese examples:

1. O remetente esqueceu-se de assinar a encomenda. (The sender forgot to sign the shipment.)
2. Já verificaste o endereço do remetente? (Have you checked the sender's address?)
3. O remetente não indicou o NIF no formulário. (The sender did not indicate the NIF on the form.)
4. Recebi um e-mail de um remetente desconhecido. (I received an email from an unknown sender.)
5. O remetente não enviou o comprovativo. (The sender didn't send the proof/receipt.)