Final answer:
The transitional sentence used by the author to shift from refuting health claims to presenting their own claim is about the environmental challenges posed by the popularity of coconut water.
Step-by-step explanation:
The sentence that the author uses to transition from refuting opposing claims to making a claim of her own is: "Aside from potentially false health claims, the surge in the popularity of coconut water poses an environmental challenge as well." This sentence shifts the focus from the health claims related to coconut water and introduces a new idea related to the environmental impact of its increased demand. By doing so, the author transitions to making their own claim regarding the environmental issues connected with coconut water's popularity.