A facelift does not typically remove skin wrinkles
If the wrinkles were caused by the alteration of your facial skin during a facelift they should go away as your plastic surgeon says. However skin wrinkles that you had before your facelift are typically caused by movement of your facial muscles and will return after surgery. Typically laser resurfacing is required to improve skin wrinkles.
Need to see the full face pictures. Better in person evaluation and review the operative report of what was done. Then we will be able to advise better. However I doubt these wrinkles will go away without a revision surgery or possibly laser resurfacing
Samir Shureih MD. FACS