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

Yes

The only differences between the use of "supor" in Brazilian and Continental Portuguese are in pronunciation. In Brazilian Portuguese, the vowels tend to be more open and the rhythm is more syllable-timed (each syllable receives more equal weight). In Continental Portuguese, unstressed vowels are much more closed or even reduced, and the rhythm is more stress-timed. The meaning, spelling, and grammatical conjugation of the verb are identical in both dialects.

Brazilian Portuguese Examples

• Eu suponho que você tenha razão. (I suppose you are right.)
• Vamos supor que ele não venha à festa. (Let's suppose he doesn't come to the party.)
• Eu suponho que a aula termine logo. (I suppose the class will end soon.)
• Você supõe que eu saiba o segredo? (Do you suppose I know the secret?)
• Não podemos supor nada sem provas. (We cannot suppose anything without proof.)

Continental Portuguese Examples

• Eu suponho que tenhas razão. (I suppose you are right.)
• Vamos supor que ele não venha à festa. (Let's suppose he doesn't come to the party.)
• Suponho que a aula termine agora. (I suppose the class is ending now.)
• Supões que eu saiba o segredo? (Do you suppose I know the secret?)
• Não se pode supor nada sem provas. (One cannot suppose anything without proof.)