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

Yes

The spelling, meaning, and grammar of "morango" are identical in both Brazilian and European Portuguese. The only difference lies in pronunciation. In Brazilian Portuguese, vowels tend to be more open, and unstressed syllables are more clearly articulated. In European Portuguese, vowels are often more closed, and unstressed vowels (such as the final "o") are frequently reduced or nearly elided, making them sound more like a short "u".

Brazilian Portuguese Examples

1. Eu adoro comer morango com leite condensado. (I love eating strawberry with condensed milk.)
2. O suco de morango está muito gelado. (The strawberry juice is very cold.)
3. Comprei uma caixa de morangos frescos na feira. (I bought a box of fresh strawberries at the street market.)
4. Essa vitamina de morango é minha favorita. (This strawberry smoothie is my favorite.)
5. Tem um pedaço de morango no topo do bolo. (There is a piece of strawberry on top of the cake.)

European Portuguese Examples

1. Eu adoro comer morango com leite condensado. (I love eating strawberry with condensed milk.)
2. O sumo de morango está muito frio. (The strawberry juice is very cold.)
3. Comprei uma caixa de morangos frescos no mercado. (I bought a box of fresh strawberries at the market.)
4. Este batido de morango é delicioso. (This strawberry smoothie is delicious.)
5. Há um pedaço de morango no topo do bolo. (There is a piece of strawberry on top of the cake.)