Was John the Baptist Elijah Reincarnated?

Question:  How do you explain the link between John the Baptist and Elijah? 

¹⁹ The Jewish leaders in Jerusalem sent priests and Levites to ask John who he was. John spoke the truth to them. ²⁰ He did not try to hide the truth. He spoke to them openly. He said, “I am not the Messiah.”

²¹ They asked him, “Then who are you?

Are you Elijah?”

He said, “I am not.”  (John 1:19-21)

A man may have glory.  A warrior on a battlefield may have done some heroic things.  Someone else claiming that they were at the battle, but were not, or claiming to do heroic things that they did not, that would be stolen valor or "Sharing in Glory."  

Elijah the Prophet was a man who did some very particular things for God's Glory.  Someone claiming to be Elijah may have been looking to share in that glory, or steal valor.  Jesus Christ did some very particular things in his life, death, and resurrection.  Someone claiming to be Jesus may have been looking to Share in Glory, or steal valor.  A Satan may have been a "Sharer of God's Glory."  There is no such thing as reincarnation in Christianity. 

John the Baptist did some pretty awesome things.  There is Glory there.  

Explaining much more ventures into some controversial revelation that is not new; however, it was controversial hundreds of years ago.  I don't know that people are ready for that, at this time. 

Enoch is to Noah as Elijah is to Elisha as Jesus is to......Not Jesus.  There is something there.  There may be been something going on the last 2000 or so years. 

Addendum

Question:  Wasn't Lucifer known as sharer of God's Glory? 

Lucifer or Morning Star may have been a title or function. 

• “How you are fallen from heaven,
  O ^[a]Lucifer, son of the morning!
  How you are cut down to the ground,
  You who weakened the nations! (Isaiah 14:12)
• “I, Jesus, have sent My angel to testify to you these things in the churches. I am the Root and the Offspring of David, the Bright and Morning Star.”
    (Revelations 22:16)  
•  ²⁶ And he who overcomes, and keeps My works until the end, to him I will give power over the nations—²⁷ ‘He shall rule them with a rod of iron; They shall be dashed to pieces like the potter’s vessels’—as I also have received from My Father; ²⁸ and I will give him the morning star.  (Revelations 2:26-28) 

  Lucifer was a Title or Function that may have to do with God's Judgement of Nations.  Satan, an Angel, he was an Accuser.  Arch Angel Michael is "Most Like God."  Arch Angel Michael has been known as mankind's advocate.  God is a judge. Satan, a fallen Angel, he coveted man.  Satan may have been like mankind's jealous step brother, looking to get man into trouble with Father God.  Jesus Christ loves you. 

Given men were worship Lucifer, a fallen angel, there may have been a demon birthed of that, or just there where man was worshiping a Lucifer.  "Lucifer" may not have been  the demon's name.  That would be Beelzebub.  I haven't studied Hebrew much, at this time, but I find the "Intersection" of Lord and Baal in Hebrew to be interesting given the Spiritual Warfare that has been going on today. 

Satan, a fallen angel, would be the dark shadowy angel figure.