Or take for example the property of Unmoved. But Jesus is God, and He has moved.
Fundamentally, I think you have a problem with the logic of Unmoved Mover or Divine Simplicity.
Feser discusses it on this thread…
edwardfeser.blogspot.it/search?q=cambridge+change
An excerpt:
Here, building on a distinction famously made by Peter Geach, we need to differentiate between real properties and mere “Cambridge properties.” For example, for Socrates to grow hair is a real change in him, the acquisition by him of a real property. But for Socrates to become shorter than Plato, not because Socrates’ height has changed but only because Plato has grown taller, is not a real change in Socrates but what Geach called a mere “Cambridge change,” and therefore involves the acquisition of a mere “Cambridge property.” The doctrine of divine simplicity does not entail that God has no accidental properties of any sort; He can have accidental Cambridge properties.
Now it was Aquinas’s position that “since therefore God is outside the whole order of creation, and all creatures are ordered to Him, and not conversely, it is manifest that creatures are really related to God Himself; whereas in God there is no real relation to creatures, but a relation only in idea, inasmuch as creatures are referred to Him” (ST I.13.7). As Barry Miller points out in his book A Most Unlikely God, this amounts to the claim that while the relation of creatures to God is a real one, the relation of God to creatures is a mere Cambridge one, so that (for example) God’s creating the universe is one of His merely Cambridge properties.
How can this be so? As Brian Davies points out in his chapter on divine simplicity in An Introduction to Philosophy of Religion (3rd edition), what is essential to acting is the bringing about of an effect in another thing, not undergoing change oneself as one does so. What is essential to teaching, for example, is that one cause someone else to learn, and not that one lecture, write books, or the like. Of course, in created things, bringing about an effect is typically associated with undergoing change oneself (e.g. for us to cause another to learn typically requires lecturing, writing, or the like as a means). But that is accidental to agency per se, something true of us only because of our status as finite, created things. We should not expect the same thing to be true of a purely actual uncaused cause of the world. Hence there is no reason to suppose that God’s creation of the world entails a change in God Himself.
To explain this differently, Cambridge properties/changes are accidental because they are only descriptive of what appears as “change” but are only relative to things that do, in fact, change. It is because our relative standing vis a vis God ”changes” that it appears to us that God is changing.
Take the idea of Jesus “becoming” man. That would only be a real change if it meant The Second Person of the Trinity took on something “foreign” to his nature. However, in Genesis it says man was created “in God’s image,” which means the essential nature of “man” derives from some aspect of God, so when Jesus became a man, it means he “lived out” or “was experienced” by human beings as that aspect or image eternally present in God in relation to other men and to the material order (a Cambridge change) when he “became man.” However, the essence of "man-ness” is contained in the very nature of God, eternally, in virtue of the fact that God is the Actuality of all Actualities.
In other words, Jesus eternally possesses “human nature” as the “image of God” in whose image all men are made. He didn’t need to “become” human by taking on new and novel characteristics he didn’t previously possess, these were merely “incorporated” in experiential relationship to human physical existence after 6 AD. We “came to know” the human nature of God in Jesus, but not because human nature is something completely foreign to God that Jesus had to “transform” himself into.
Recall that for Aquinas, God is Pure Act, the fullness of all Being, so the essence of “humanity” is eternally within the “image of God” (Jesus, the Logos, the Word) from eternity. He didn’t take on something essentially different from the divine essence, but “lived out” the aspect of that image relative to human existence on Earth - a Cambridge change, one that does not require undergoing change oneself; hence remaining Unmoved Mover. Recall: “…what is essential to acting is the bringing about of an effect in another thing, not undergoing change oneself as one does so…”
Jesus, “walking the Earth,” was essentially his bringing about the effect of humans seeing, hearing, touching, etc., him “as man,” but as “man” in the sense of Imago Dei, the image of God eternally subsistent as an aspect of God’s nature. The change did not require actual change in God, but in how God was seen or otherwise appropriated by human beings.