While the sentence in itself is correct but it does not use a conjunctive adverb. False.
Explanation:
Conjunctive adverbs like However, therefore etc are used to connect two independent clauses but they do not join or merge them into the same sentence.
There must always always be a semicolon before and comma after a conjunctive adverb.
Here the sentences are simply joined with a but and makes complete grammatical sense so any other word is not needed to complicate the sentence.