Tenant with a theft charge and Cosigner

Hello,

I recently came across a tenant application and while checking the background is noticed that a theft charge, judgements and other collection reports. But the situation here is the tenants mother is renting the unit and renting for the tenant. So I checked the mothers background and everything is perfect.

So I would like to know whether it is OK to rent the unit to the applicant with such a history even though some one else is renting the unit for them?

In this case, when you sign the lease, does the mother is part of the lease or does she become a co-signer. Since mother is responsible for paying the rent even though she does not staying in the house, she should be part of the lease right?

Thanks
DJ