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

Yes

The spelling, meaning, and grammatical conjugation of "ensinou" are identical in both Brazilian and Continental Portuguese. The differences are limited to:

• Pronunciation: Brazilian Portuguese tends to use more open vowels, whereas Continental Portuguese often features more closed or reduced vowels.
• Syntax: While the word itself is unchanged, its usage in a sentence with object pronouns differs. Brazilian Portuguese typically uses proclisis (e.g., "me ensinou"), whereas Continental Portuguese typically uses enclisis (e.g., "ensinou-me").

Brazilian Portuguese

1. Ele me ensinou a dirigir. (He taught me how to drive.)
2. Minha mãe ensinou tudo o que eu sei. (My mother taught me everything I know.)
3. O professor ensinou a matéria de um jeito fácil. (The teacher taught the subject in an easy way.)
4. Ela ensinou o cachorro a sentar. (She taught the dog to sit.)
5. Ele ensinou as regras do jogo. (He taught the rules of the game.)

European Portuguese

1. Ele ensinou-me a conduzir. (He taught me how to drive.)
2. A minha mãe ensinou-me tudo o que eu sei. (My mother taught me everything I know.)
3. O professor ensinou a matéria de uma forma fácil. (The teacher taught the subject in an easy way.)
4. Ela ensinou o cão a sentar. (She taught the dog to sit.)
5. Ele ensinou as regras do jogo. (He taught the rules of the game.)