Hi,
In Buddhism, it is rebirth, not reincarnation. There is a difference but it is not critical for someone starting to learn Buddhism.
Things of this type cannot have absolute “proof” but there is evidence to support rebirth:
“Evidence for Rebirth”
Regarding my comment above, see, “What Reincarnates? – Concept of a Lifestream”
Please feel free to ask questions on any of these posts. It would be easier if you refer to the post particular bullet number in question (unless it is a general question).