They finished their building by decree of the God of Israel; and by decree of Cyrus and Darius, that is Artaxerxes, king of Persia.Darius was questioned about the existence of a previous decree of Cyrus which was found in the archives and reinstituted by Darius with further stipulations. And Cyrus' decree is that of God's decree as prophesied in Isaiah,
Thus says the LORD, your Redeemer,/So we have a decree of God and he tells us it will come thru Cyrus. Cyrus gives a decree.
who formed you from the womb:/
"I am the LORD, who made all things,/
who alone stretched out the heavens,/
who spread out the earth by myself,.../
who says of Cyrus, 'He is my shepherd,/
and he shall fulfill all my purpose';/
saying of Jerusalem, 'She shall be built,'/
and of the temple, 'Your foundation shall be laid.'" (Isaiah 44)
Then we have a request for the decree of Cyrus to be checked. Darius confirms Cyrus' decree and reiterates and expands on it.
The suggestion that Artaxerxes is a different king to Darius precludes a single decree.
I don't think this is an argument (or at least a strong one) for Darius to be identified as Artaxerxes, more an interesting conclusion if this happens to be the case.
Part 1. Part 2. Part 3. Part 4.