There is no true or false!

Either you believe it or not.

It is also dependents on how reincarnation is defined. I am not a Christian, but I think the Christian idea of reincarnation differs eg from the ideas of reincarnation in Asian religions.

If there is ever a Christian idea of reincarnation.

Referring to the Christian doctrines the only Reincarnation I know is likely to be no one following Christian terms, i guess. Namely, the reincarnation of God in a man called Jesus Christ.