Whether or not the original lessee is liable once the lease is transferred depends on the leasing company involved.
Some leasing companies completely remove the first individual from the account and some choose to leave the original lessee liable as a guarantor.
When the original leaseholder is removed, the lease transfer is typically referred to as a “lease assumption”. When liability remains with the original lessee, the process is known as a “transfer of equity”.
Within North America, its quite typical the lease agreement and conditions are fully transferred to the Lease Seller. In the view of the leasing company, if they’ve performed the credit check and find the Lease Buyer is credit worthy, they would have a better legal chance of getting the ongoing lease payments from them, versus chasing the previous Lease Seller who typically exited the lease due to financial difficulties. It can be in the best interest of the leasing company to allow a lease transfer if the other person is more credit worthy. However, due diligence should be done to confirm with your leasing company.