Reincarnation Round 1: Jesus said John the Baptist is Elijah

In the old Testament, Mal 4:5 mentioned that Elijah would come before the coming of Jesus Christ.

In the new Testament, Luk 1:17, the angel told Zacharias that his son (John the Baptist), is the forerunner Jesus Christ. Luk 1:76 says "you child will be called the prophet of the Most High; for you will go on before the LORD to prepare His ways."

In Matt 11:14 and Matt 17:12, Jesus explicitly explained to his disciples that he (John the Baptist) is Elijah.

The prophesy in Mal 4:5 that Elijah must come before Jesus Christ must be fulfilled. Elijah's spirit/soul came in the physical body of John the Baptist. This is an example of reincarnation.

So in Round 1 of this series of study on Christian Reincarnation, I conclude that reincarnation is possible.