Sentence A is correct because when you have a conjunctive adverb linking two independent clauses, you should use a semicolon. In this case, both of these independent clauses have been connected by the conjunctive adverb <em>however</em> (see 1 and 2). What is more, you should use a comma after the conjuctive adverb because it appears in initial position in the second clause.
1) She tried to pain the building; (independent clause I)
