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

No.

While the spelling and fundamental meaning of "ler" (to read) are identical in both dialects, there are significant differences in typical usage, syntax, and the way the word interacts with other parts of a sentence. In Brazil, when expressing a continuous action, the gerund form "lendo" is used, which replaces the word "ler" entirely. In Portugal, the prepositional infinitive construction "a ler" is the standard, meaning the word "ler" is preserved in that context. Additionally, there are differences in how "ler" is paired with pronouns (clitics) and prepositions.

Brazilian Portuguese Examples

1. Eu adoro ler antes de dormir. (I love to read before sleeping.)
2. Você pode ler este aviso para mim? (Can you read this notice to me?)
3. Eu estou lendo o livro que você me deu. (I am reading the book you gave me.)
4. Ele esqueceu de ler o e-mail. (He forgot to read the email.)
5. Precisamos ler o manual com atenção. (We need to read the manual carefully.)

Portuguese Examples

1. Eu adoro ler antes de dormir. (I love to read before sleeping.)
2. Podes ler este aviso para mim? (Can you read this notice to me?)
3. Estou a ler o livro que me deste. (I am reading the book you gave me.)
4. Ele esqueceu-se de ler o e-mail. (He forgot to read the email.)
5. Precisamos de ler o manual com atenção. (We need to read the manual carefully.)