The guaranteed way to suffice your finance agency's smog check certificate requirement, since the vehicle's previous owner does not have a hard copy, is to visit the smog station where the vehicle was inspected, and ask for a copy of the certificate. They may be able to print it out from their smog machine (computer system) or give you a copy from their records.
Should this not be practical, maybe the smog station is out of town or no longer in business, the next best option would be to search the BAR Smog Check History results. From there, you can print out a screenshot of yur vehicle's smog history. The BAR Smog Check History will show your vehicle's smog check PASS or FAIL smog status, and if passed, display to you the smog certificate number. Hopefully this will be enough to satisfy your finance company's proof od smog check requirement.
BAR Smog Check History
For vehicle registration and title transfer purposes, the DMV in most circumstances, will not require a hard-copy of your vehicle's smog check results, meaning a "smog certificate" or Vehicle Inspection report (VIR). A "hard copy" of your vehicle's smog certificate (also known as the Vehicle Inspection Report) can be obtained only from the smog station which inspected your vehicle.
Contact the smog station where your vehicle was inspected. Smog certificate information is kept in electronic format in the VID (Vehicle Information Database) which is run by the State of California Bureau of Automotive Repairs, and looked over by the California Air Resources Board. Once a vehicle receives an official smog check, the smog inspection data, including pass or fail results, are stored with the State and available to government entities, such as the California DMV, indefinitely. A smog station is required to keep hard copies of smog certificate for a period of three years.