Assuming a lot of things, like this is a fumble during a scrimmage down, with no 4th down fumble rule involved, with no legal kick involved, then, yeah, that is correct. A fumble by A, recovered by A, and there is no other reason to stop the game clock, then the play clock is set t0 40, and starts after the ball becomes dead from the previous down.
Simplified answer to a somewhat complex scenario.