The prepositions are the words which show the relationship between the pronoun and the nouns. On the other hand, the prepositional phrase starts with the prepositions and end with the object of a preposition, having one or more modifiers to describe.
Adverb phrase refers to the group of words which qualifies adjectives, verbs or adverbs.
While answering the question of where? when? or how? prepositional phrase is identified as an adverb.
Therefore, the sentence in which group of words is a prepositional phrase acting as an adverb is My sister applied [on Tuesday] to a graduate school in England.
As the above bracketed sentence answer the question of when did she apply? - 'on Tuesday', hence it qualifies to be a prepositional phrase acting as an adverb and modified 'applied.'