power brake booster check valve

Okay, I heard something that needs clarifying;
"The pedal gets hard maybe half way in it's travel. With the engine running the pedal and the pedal is pumped gets higher and higher but still deflects some."
-This could be normal, or not.There are two possibilities here; 1) If the brake shoes are a little loose and/or if there are 4 sets of them, then each pump pushes a little fluid out, which pushes the shoes out a little. Then when you release the pedal, the residual valves slow the return of the fluid. And an immediately following pump again pushes a little fluid out. And so on. Eventually the shoes are out as far as they can go, having reached the drums and put the pressure to them; and the pedal is hard, right at the top of its stroke. So far so good. But now comes the important part. If you now remove your foot to release the pedal, and it returns to it's parked position, then the return springs inside each drum should return all the shoes to their pre-applied condition, and forcing all that fluid back to the M/C. The pedal should now, again be soft. This is very important. It proves the pushrod is NOT too long.
2) If the pushrod is too long, it may not allow the fluid to return to the M/C. In this case the pedal gets hard after the pumping, and may or may not ever return to the former softness, after removing the foot ; it kinda depends on how much too long it is. Just a hair too long, and the fluid may return after some amount of time goes by. If it is more than about 1/16 too long, the compensating port will be blocked, and no fluid can return.
In either case if the pedal remains at the top or less than about 50% travel the pushrod may never reach the vacuum valve to operate it.
The pedal can remain hard overnight and longer.
So let's get that out of the way first. Does the pedal get soft again? Does it return to it's parked position?
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Now; This is how a good booster should work;It assumes the rest of the system is working properly, and the brake shoes are properly adjusted.
With the engine off, Pump the brakes about 5 or 6 times to bleed any trapped vacuum away that may be stored in the booster.( in your case if the vacuum check valve is bad,pumping would not make a difference). Next, put about 30 or 40 pounds of foot pressure on the pedal, and start the car. Right after the car starts a working booster will drop the pedal, under your foot pressure, about an inch and a half, give or take.
If it does that it's good.
If it doesn't do that it MAY be bad. So what to do? Undo the booster retaining nuts and pull the booster away from the firewall, just enough to see the pushrod. Find the adjusting nut on the end, and turn it CW from the driver's seat; 6 flats or 1 turn, to make it longer. Reattach the booster. Retest.Do not mash the brake pedal, as it is possible to brake the internal valve and then, for sure, the booster will be bad. If you feel resistance in the foot pedal, that is different from before, DON'T force it. Ok, start the engine.
Any difference? If the pedal now drops, you are in the ballpark. From here you can adjust the pushrod length to give you just the amount of boost you like, by fine tuning it. If no difference, repeat the adjustment a half a turn longer.Once you get close it does not take much to become too long, So easy does it.
So, good luck.