"When Michael the archangel, disputing with the devil, contended about the body of Moses, he durst not bring against him the judgment of railing speech, but said: The Lord command thee." St. Jude 1:9
This quote is from the book The Assumption of Moses, one of the Apocrypha. Jude plainly states that St. Michael contended with the Devil for the body of Moses; obviously it was he, and not the devil, who won:
And after six days Jesus taketh unto him Peter and James, and John his brother, and bringeth them up into a high mountain apart: And he was transfigured before them. And his face did shine as the sun: and his garments became white as snow. And behold there appeared to them Moses and Elias talking with him. (St. Matthew 17:1-3)
I don't find NT writings to be inspired, but be that as it may and for arguments sake....your conclusion from Jude is an interpretation. Michael and Satan can dispute over a body without one or the other taking it somewhere. Perhaps Michael wanted in left there. And its not conclusive at the transfiguration that Moses was there in physical form.