B is a sentence fragment. Sentence fragments are groups of words that look like sentences, but aren't. In order to be a sentence, groups of words need to have at least one independent clause. An independent clause is any group of words that contain both a subject and a verb and can stand on its own as it represents a complete thought. Sentence fragments never have independent clauses, but instead are dependent clauses or phrases. In this case, B is a sentence fragment. It contains a subject, the NP "Mary" modified by a what-it-appears-to-be an appositive phrase (an excellent basketball player), but it lacks the predicate.
The answer is A to confirm that the passage is not yet finished. it’s the only one that make sense seeing that fact the More In furthermore is indicating that there is more to be told about something