@scottbeau, it’s great to hear the opportunity you are having to discuss matters of faith with your colleague. Though we have discussed this topic previously, I thought I can share some brief thoughts on the angle of your specific question on reincarnation.
My hindu family also has confused resurrection with reincarnation previously. As reincarnation is described as migration of the same soul through different physical bodies, resurrection where a soul receives a new (imperishable) body can be viewed by a reincarnationist the same way. For a reincarnationist, identity comes solely from the ‘soul’ unlike the Christian view where personhood is defined by ‘soul/spirit + body’. So when we say reincarnation is coming back as a different person over and over again, they will argue it’s the same person, as identity of the soul is same in different bodies. The example that is often used is of a baby growing into an adult, where the physical body looks different with age but the soul remains the same in the body. This idea is used as an argument for the possibility that a soul can migrate through different bodies even after death. Because of how they view the identity of a person, the reincarnationist focuses only on liberation of soul from the cycle of reincarnation and sees no need for redemption of body and soul as a unit and trivializes the necessity of resurrection.
So, first I might explain that in resurrection the soul receives imperishable bodies fit for the kingdom of heaven unlike the natural perishable bodies on earth (1 Cor 15). The hope of resurrection is for those who are born again by the Spirit of God through faith in Christ, which is founded on the historical resurrection of Christ. No matter how many earthly lives we have, unless the Spirit of God fills us with His life, we cant go on to live with God as we are all spiritually dead in our souls in our sin. Resurrection is about the Spirit of God redeeming our souls and bodies. God wants to redeem us a whole- Spirit and body.
Then, I might ask a few questions to establish the importance of identity in both body and soul - What role does the body play in the identity of an individual? If identity comes mainly from the soul, then how does our physical life here on earth carry intrinsic worth? What difference is there between an animal and human - is the difference only in the soul or body as well?
I hope that will serve as a start to the conversation. Look forward to any additional thoughts or questions you may have.