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

Yes

The word "escrever" is identical in meaning, grammar, and spelling in both Brazilian and Continental Portuguese. The primary difference lies in pronunciation. In Brazilian Portuguese, the unstressed vowels tend to be more open and clearly articulated. In Continental Portuguese, unstressed vowels (like the "e" in the middle of "escrever") are often reduced, closed, or even swallowed, making the word sound more clipped or "shorter" to a Brazilian ear.

Brazilian Portuguese Examples

1. Eu vou escrever uma carta para a minha avó. (I am going to write a letter to my grandmother.)
2. Ele esqueceu de escrever o endereço no envelope. (He forgot to write the address on the envelope.)
3. Você pode escrever seu nome aqui, por favor? (Can you write your name here, please?)
4. Ela adora escrever poesias no tempo livre. (She loves to write poems in her free time.)
5. Preciso escrever um e-mail para o meu chefe agora. (I need to write an email to my boss now.)

Continental Portuguese Examples

1. Eu vou escrever uma carta para a minha avó. (I am going to write a letter to my grandmother.)
2. Ele esqueceu-se de escrever a morada no envelope. (He forgot to write the address on the envelope.)
3. Podes escrever o teu nome aqui, por favor? (Can you write your name here, please?)
4. Ela adora escrever poemas no tempo livre. (She loves to write poems in her free time.)
5. Tenho de escrever um e-mail para o meu chefe agora. (I have to write an email to my boss now.)