He may have what’s called an extensor tendon lag. Complete tears of the central extensor tendon cause a disruption of the tendon fibers. Even with surgery, healing may not restore normal function and motion of the tendon. The result can be the lag you’ve noticed.
Therapy with a certified hand therapist may be needed. This is either a physical or occupational therapists who has had specific training with problems like this.
For some people an extensor tendon lag is only a cosmetic problem. Grip strength may be less than normal. Function is often normal to nearly normal. Children under the age of five with complete lacerations have more problems with extensor lag than older children or children with a partial tendon tear.
Your surgeon may be able to give you a better prediction of long-term results. Age and location and extent of the injury are the main determining factors of final outcomes.