And then Mussolini had some 6,000 Jews sent to Auschwitz.
Yes, eventually all “fascists” kissed up to Hitler. One of the more tragic cases of this was Oswald Mosley in Britain, who eventually fell under Hitler’s spell, and allowed the BUF to turn anti-semitic, while it didn’t necessarily start out that way.
Was that while he was still in power, or after he became Hitler's puppet in late 1943?
The Fascist Grand Council ejected Mussolini from power in July 1943, but Hitler had him rescued from prison in September and reinstalled him as leader of Northern (Germany controlled) Italy. By then Mussolini was no longer calling the shots, but was only Hitler's figurehead.