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

Yes

The word "falta" is identical in meaning, grammar, and spelling in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. In Brazilian Portuguese, the vowels are generally more "open" and clearly articulated. In Continental Portuguese, unstressed vowels undergo a process of reduction, meaning the 'a' sounds are much shorter, more closed, and more neutral (sounding more like a short "uh").

Brazilian Portuguese Examples

1. Ele faltou à aula hoje. (He missed class today.)
2. A falta de água é um problema grave. (The lack of water is a serious problem.)
3. O juiz marcou uma falta no jogo. (The referee called a foul in the game.)
4. Eu sinto muita falta de você. (I miss you very much.)
5. Falta dinheiro para o almoço. (There is a lack of money for lunch.)

Continental Portuguese Examples

1. Ele faltou à aula hoje. (He missed class today.)
2. A falta de água é um problema grave. (The lack of water is a serious problem.)
3. O árbitro marcou uma falta no jogo. (The referee called a foul in the game.)
4. Sinto muito a tua falta. (I miss you very much.)
5. Falta dinheiro para o almoço. (There is a lack of money for lunch.)