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

Yes

The word "falaram" is identical in meaning, grammar, and spelling in both Brazilian and Continental Portuguese. It is the third-person plural form of the verb falar (to speak/to talk) in the pretérito perfeito do indicativo (past tense). The only differences between the two varieties lie in pronunciation.

In Brazil, the vowels tend to be more open, and the "r" sound can vary significantly depending on the region (ranging from a soft tap to a retroflex "r"). In Portugal, the vowels are typically more closed, and the rhythm of the sentence is more stress-timed, which can make the unstressed syllables in "falaram" sound more reduced or "swallowed" compared to the more melodic Brazilian pronunciation.

Brazilian Portuguese Examples

1. Eles falaram que o ônibus está atrasado. (They said the bus is late.)
2. Falaram que o pessoal ia chegar tarde. (They said the folks/people were going to arrive late.)
3. Eles falaram de você na escola. (They spoke about you at school.)
4. Falaram que o café da manhã é servido às oito. (They said breakfast is served at eight.)
5. Eles falaram que o celular avariou. (They said the cell phone broke.)

European Portuguese Examples

1. Eles falaram que o autocarro está atrasado. (They said the bus is late.)
2. Falaram que a malta ia chegar tarde. (They said the group/folks were going to arrive late.)
3. Eles falaram de ti na escola. (They spoke about you at school.)
4. Falaram que o pequeno-almoço é servido às oito. (They said breakfast is served at eight.)
5. Eles falaram que o telemóvel avariou. (They said the mobile phone broke.)