If it can be said that prayer allows us to share the life of the Trinity, and I do think this is true of some kinds of prayer, then it may also be said that prayer incorporates us into divinity. If it "incorporates" us, who already have a body, then in a sense, God is incarnated in His adopted children. It is this divinization or incarnation that makes us fully part of the mystical body of Christ and it happens to each of us in greater or lesser degree (as God wills) when we turn our hearts to Him in prayer.
Keep in mind this is not theology, nor is it a studied remark. I'm completely insufficient to the task of attempting to explain how this might happen or even if I have phrased it properly. And I stand open to correction of my terminology or phrasing. But I think it is reasonable to say that prayer opens the door to Divine life here and now. And prayer starts with praying--old and well-worn words, tradtional prayers, or traditional forms. But I think we must keep in mind that is where prayer begins. It is not where prayer ends. The end of Prayer is the possession of God Himself in His entirety. In some sense by becoming His, He becomes ours entirely. When we set His seal upon us, He gives Himself to us in all of His majesty. We cannot see it, nor can we fully know it--this is what all of the Dark Night is really about--His brilliance is night to the senses and intellect, but when we are there He is Ours and we are His.
"I am my beloved's and He is mine."
