No. You cannot use "however" to join two independent clauses into a single sentence. That word has nothing to do with how compound sentences are formed.
It is very common to see transitional adverbs like "however", "therefore", "additionally" and "consequently" immediately following a semicolon. However, that semicolon joins those clauses without any help from any word in either clause. That's the way things work; semicolons are enough. Additionally, such transitional adverbs are commonly found at the beginning of simple sentences such as these two. Therefore, there is little to justify calling them conjunctive.
It is not always necessary, however, when we use it to link two parts of that instrument.
In the absence of context, there is no error in this sentence, although it might not mean what you think it means. This "however" is a supplement of the main clause. It carries the same meaning and has the same relationship to the main clause even if it is moved to the beginning of the sentence:
However, it is not always necessary when we use it to link two parts of that instrument.
Without context, we have no idea what the referent of each "it" might be. We have no available antecedents for them. They do not share their referent. The first seems to be a semantic practice or behavior; the second a method or implement.
Having moved "however" from the middle of the sentence, we've also removed the reason for any punctuation in front of the subordinate clause.
Can we use a subordinating conjunction after a conjunctive adverb? Well, no, not if there's no such thing as a conjunctive adverb.
Can we use a subordinating conjunction after a transitional adverb? Sure. Why not? The sentence would need to be otherwise sound, but there is nothing that prevents that arrangement.
Does using a subordinating conjunction after a transitional adverb create a compound sentence? No. The subordinating conjunction helps create a complex sentence, no matter where or even whether a transitional adverb appears.
