Didn't the incarnation change God?

I’ve got an interesting question posed by a Mormon friend of mine that I need help on.
They believe Christ had to obtain a body in order to become a God.

His question is this:

If God was always God and always omnipotent, then doesn’t the incarnation change God somehow? Doesn’t it add to God something that He didn’t have prior to the incarnation? Then how was He omnipotent and unchangeable prior to the incarnation if after it He now has a body?

Any help is appreciated!

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Did the Incarnation of Christ change God?

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