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If I believed like you seem to, he would share the body Christ got, after all, they are the same person and if one does something, they all do it.
Now, if you are referring to the GOD HEAD, the Holy Spirit will get his body when it is his time.
There you go again, misstating Christian doctrine (but I'm used to that here). Still didn't answer the question - mormon doctrine teaches that inorder to attain godhood, one must pass through mortality. The Holy Spirit, according to mormonism, is a personage of spirt - with out a body. So the question still stands - how can the HS be a God with out getting a body?