My first rental property - updating the lease agreement

[Jonathan Mulkey]

I'm a new investor based in Chattanooga, TN. I just closed on my first rental property and it is tenant occupied. I'm in the process of setting up the new lease agreement and I want to keep the terms the same as the previous owner. They have been there for 2 months already and they paid the security deposit and this month's rent to the previous owner. What is the best way to update the lease agreement and should I ask the previous owner to transfer the funds for the security deposit and pro-rated rent for this month?