The question contains an unstated assumption: In Eph 1:1, "God" is God the Father. This assumption may not be correct.
Note that in the Greek, "theos" (= God) lacks the article. If it had the article, then there would be a reasonable case (but far from conclusive) that "God" here would refer to God the Father (eg John 1:1, etc).
However, the fact that in Eph 1:1 "God" lacks the article, suggests the probability that the Godhead more generally, is in Paul's mind.
For more examples of this see such verses as 2 Cor 2:17 where both forms are used. David Bentley Hart, in his appendix to his translation of the New Testament has some very helpful comments about the distinction between the articular and inarticular (or arthrous and anarthrous) forms of theos.