Tenant wants to sublet, how do we do this?

[Greg W.]

So my tenant wants to sublet the house she just rented three months ago. We are thinking of having the tenant find the sublessor and we will still use our criteria to vet the sublessor and approve them.

1. Should there be a separate sublease agreement for the new subletting tenant or should the subletter just sign onto the original lease as a sublessor? 

2. Should we, the landlord, get the security deposit from the sublessor or should the sublessor give the security deposit to the current tenant?

3. Should the sublessor pay the tenant and tenant is still responsible for paying us, the landlord, or should the sublessor pay us, the landlord, directly?

We are thinking of having the tenant find the sublessor, we will still use our criteria to vet the sublessor and approve them.

Anything else we should think about?