The process, I believe, is that the Light or Spirit of Christ takes the place of the Holy Ghost; the Holy Ghost takes the place of the Christ or the Son; and the Son takes the place of the Father in the next eternity or iteration. And the Father? Alma 37:11

If the Holy Ghost is a "personage of Spirit" and it can "dwell in us," and the Holy Spirit is "the mind of the Father and Son" then are they the same thing?

The scriptures have explained that the "Holy Ghost" which dwells in you - this personage of Spirit - has the following other descriptions, or attributes:
-the Comforter
-the record of heaven
-the truth of all things
-the peacable things of immortal glory
-that which quickeneth all things
-that which knoweth all things
-that which has all power according to wisdom, mercy, truth, justice and judgment.
(Moses 6: 61.)
This is a description of the personage of Spirit which dwells inside you. This is the Holy Ghost. This is something that can be in contact with the Holy Spirit, or the "mind of the Father and Son."