Scored my first deal!! Some questions..

[Kristopher Shobe]

I just submitted my deposit on a rental property, so excited!! The current tenants have a lease with the current owner. When closing comes, do I take a brand new lease to the tenants and hope and pray they sign (I want them to stay) or do I present them with their current lease but just with my name instead of current owners? Then when their current lease expires which is march of next year, then present a new and improved lease. Yes I have done research. Months to be exact, but this wasn't covered.

Thank you all!!