Best way to transfer existing tenants from one property to another

[Bienes Raices]

I have some tenants in one house who have been paying on time, but they would like a cheaper place to live. I am closing on another property soon that will be about $100 cheaper in rent. But since the prospective tenants are supposed to hold the other property with a deposit in advance, but I cannot give them their security deposit back for the house they are currently living in until they are out of there, I'm not sure if they'll be able to put down an extra deposit.

In addition, the house they live in now is owned in my personal name, but the new house will be owned by an LLC.

Is there a good way to do this?