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

Yes

The word "dever" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only differences are phonological. In Continental Portuguese, unstressed vowels are significantly more reduced (often becoming almost silent), and the rhythm is more stress-timed. In Brazilian Portuguese, vowels are generally more open and the rhythm is closer to syllable-timed, making the word easier to distinguish clearly in speech.

Brazilian Portuguese Examples

1. Você deve estudar para a prova. (You must study for the exam.)
2. Eu devo cinquenta reais para ele. (I owe him fifty reais.)
3. Eles devem chegar logo. (They should arrive soon.)
4. Nós devemos respeitar as regras. (We must respect the rules.)
5. Você deve me avisar quando chegar. (You must let me know when you arrive.)

Portuguese (Portugal) Examples

1. Tu deves estudar para o exame. (You must study for the exam.)
2. Eu devo cinquenta euros a ele. (I owe him fifty euros.)
3. Eles devem chegar em breve. (They should arrive soon.)
4. Nós devemos respeitar as regras. (We must respect the rules.)
5. Deves avisar-me quando chegares. (You must let me know when you arrive.)