If an organism has high biological fitness in one environment, does that mean that it would also have high biological fitness in another environment? Why or why not?

The answer is no, high biological fitness in one environment doesn't have to be high in another environment.

Biological fitness is a term used in evolutionary biology and it is the quantitative representation of how a genotype (or phenotype) is successful (reproductively) in a certain environment. Fitness depends on environment so it changes if the environment changes. The fitness of a genotype is manifested through its phenotype, which is affected by the environment.