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

Yes.

The word "recuperar" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The only differences are phonetic. Brazilian Portuguese tends to have more "open" vowels and a more melodic, syllable-timed rhythm. In Continental Portuguese, unstressed vowels are much more "closed" and often reduced or nearly silenced, resulting in a more stress-timed rhythm.

Brazilian Portuguese Examples

1. Ele está se recuperando de uma gripe. (He is recovering from a flu.)
2. Não consigo recuperar minha senha. (I can't recover my password.)
3. Eu recuperei meu celular ontem. (I recovered my cell phone yesterday.)
4. O time conseguiu recuperar o placar no segundo tempo. (The team managed to recover the score in the second half.)
5. Eu preciso recuperar o dinheiro que emprestei. (I need to recover the money I lent.)

Continental Portuguese Examples

1. Ele está a recuperar de uma gripe. (He is recovering from a flu.)
2. Não consigo recuperar a minha palavra-passe. (I can't recover my password.)
3. Eu recuperei o meu telemóvel ontem. (I recovered my mobile phone yesterday.)
4. A equipa conseguiu recuperar o marcador no segundo tempo. (The team managed to recover the score in the second half.)
5. Eu preciso de recuperar o dinheiro que emprestei. (I need to recover the money I lent.)