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

Yes

The word is identical in spelling, meaning, and grammatical category (3rd person singular indicative and 2nd person singular imperative). The only difference is pronunciation: Brazilian Portuguese features more open and distinct vowels, whereas Continental Portuguese involves significant vowel reduction, often making the unstressed final "e" sound like a very short "i" or even becoming nearly silent.

Brazilian Portuguese

1. Você escreve muito bem. (You write very well.)
2. Ele escreve um e-mail agora. (He is writing an email now.)
3. Ela escreve poesias lindas. (She writes beautiful poems.)
4. Escreve seu nome aqui. (Write your name here.)
5. Ninguém escreve no quadro. (No one writes on the board.)

Continental Portuguese

1. Tu escreves muito bem. (You write very well.)
2. Ele escreve um e-mail agora. (He is writing an email now.)
3. Ela escreve poesias lindas. (She writes beautiful poems.)
4. Escreve o teu nome aqui. (Write your name here.)
5. Ninguém escreve no quadro. (No one writes on the board.)