score:7
There is nothing in LDS canon about this, as far as I can tell. There are a couple statements from Joseph Smith that indicate that he felt the Holy Ghost would eventually receive a body, which I've copied from the linked article. The first is from the Encyclopedia of Joseph Smithβs Teachings:
The Holy Ghost is yet a spiritual body and is waiting to take to himself a body, as the Savior did.
And the second is from the Words of Joseph Smith:
The Holy Ghost is now in a state of probation which if he should perform in righteousness he may pass through the same or a similar course of things that the Son has.
You would have to check the referenced print sources to obtain more detail on the context of these quotations.
However, note that other general authorities have failed to confirm these statements as doctrine, and have stated that there is nothing authoritative on the matter (see this link). Generally, a church leader, even Joseph Smith, making a couple of statements on a given topic doesn't automatically mean they are doctrine. In the case of Joseph Smith's recorded statements on the Holy Ghost receiving a body, we do not know if these statements are revelation or speculation.
Upvote:1
Short answer: Either after everyone else, or sometime after Christ comes again.
Either he is required until the very end and will be the very last of all God's children to receive a body, or he is only required until Christ (the second comforter) returns during the Millennium.
However, there is no firm answer. Bruce R. McKonkie said this in regards to the Holy Ghost:
In this dispensation, at least, nothing has been revealed as to his origin or destiny; expressions on these matters are both speculative and fruitless - (Mormon Doctrine)
If the Holy Ghost is a spirit Child of God, just like everyone else, then he will be resurrected, just like everyone else. The only spirits who will never be resurrected are those who kept not their first estate; the sons of perdition.
If the Holy Ghost is not a child of God, then we have no idea who he is, where he came from, or why he is still a spirit. There is limited progression as a spirit, hence why we're all sitting here on earth in our mortal meat suits talking about spiritual matters on the internet. There is little reason to believe that he is not a child of God.