American Heritage Dictionary says it, but this explanation of "But" usage as a
preposition and the change of pronoun cases does not have any bearing on how "However" is used in place of "But."
Use "But" as a coordinate conjunction to join two independent clauses (simple
sentences).
Use "However" either as a conjunctive adverb (after semicolon in a compound sentence) or as an expression to introduce transition of ideas. If the first sentence is too long (more than 15-20 words with lots of intervening adjective phrases, adverbial phrases), you can start the second sentence with "However." Note that "However" is an adverb - it is called conjunctive adverb because it serves the purpose of a conjunction in a compound sentence by joining two independent clauses (independent ideas).
However, you can use "However" to start a sentence.
"However" in place of "But."
