The buff helps, but the MP40 still depends on reaching the right range without giving away too much health.
Close with cover
Use walls, elevation and lateral movement. Crossing open ground against rifles wastes the MP40's advantage.
Do not empty the magazine
At medium range use short bursts or switch weapons. Better accuracy does not turn it into a rifle.
Use the faster swap
Swap to a shotgun or rifle before getting caught in a long reload.
Official sourceOfficial reference